"Doo wop" is a recent term for a type of early rock and roll that used vocal harmony with minimal instrumentation.
Vocal harmony uses voices offset from each other in timing, but melodically so :-).

Vocal harmony in the doo-wop context began in the late 40s, and flourished as rock and roll from about 1954 through 1961. However, the term - while heard in some of the early songs - was not used until years later when the performances became quite popular again.

These elements are commonly heard in doo-wop performances, in addition to the essentials of group harmony not in the lead, minimal instrumentation, and being rock & roll:
- nonsense syllables (such as "doo wop"), often used to simulate musical instruments
- progressive entrances of the voices
- a wide range of voices, often including a falsetto voice (sometimes seeming to "float above" the bass lead, more commonly the lead) and usually a bass voice (typically punctuating and/or "under" the other singers, but sometimes the lead. (We are talking real bass here, low low low :-) The high-low combination is called "top and bottom", introduced by Bill Kenny.
- talking through the bridge (the "instrumental" part in the middle)
- or an instrumental solo in the bridge (often a saxaphone)
- a talking introduction is noteworthy but less common than the foregoing

The test being "can this be sung by teenagers on a street corner?"
(Apparently they are again doing so in New York City.)

PEDANTIC DETAILS:

Rock & roll (later "rock" music is not "rock & roll" :-), generally includes:
+ strong beat
+ simple beat (for doo-wop that suits "snapping & clapping" on the street corner)
+ simple lyrics (but Motown told a story in each of their earlier songs :-)
+ positive and/or life-oriented (well, perhaps not One Last Kiss nor Moody River :-), but notably different from Rythm and Blues - some R&B DJs called it "Happy Music")
+ teenage themes, especially romance.

Examples of doo wop hits that you might recognize:
- In the Still of the Night, by the Five Satins
(a garage demo recording that was a smash hit as-is)
- Only You, by The Platters
- Barbara Anne, by the Regents
(but the Beachboys made a reasonable "cover" version by being faith to the original (early Beach Boys efforts can be called doo wop, and somewhere along the way they had fun with voice overlays in Sloop John B).
- Only You, by the Platters
- A Thousand Miles Away, by the Heartbeats (the Diamonds' cover is fine)
- Since I Don't Have You, by the Skyliners
- Sixteen Candles, by the Crests
- Duke of Earl, by Gene Chandler
- I Wonder Why, by Dion and the Belmonts
- The Lion Sleeps Tonight, by the Tokens
- White Christmas, by Clyde McPhatter and the Drifters (with both high and low leads)
(Later I'll include lesser known productions that are more characteristic of doo-wop.)

Note it's the performance that is doo wop, not the song per se. Many groups performed both doo wop and other styles, and many songs were performed both ways though not necessarily well. (If someone offers to play Unchained Melody by Vito and the Salutations you should run away. :-) [But, sorry, I don't think the great Righteous Brothers hits were doo wop. Though some may consider that a good thing. ;-] But its hard to pigeon-hole any "type" of music.
Of course bits of vocal harmony are found here and there in popular singing. For example, in the earliest of the Supremes hits for Motown. That was such a major value for them that earlier they tried to keep four members in the group despite the usual attrition. (The Supremes came out of an environment where teenagers were singing in the courtyards of apartment complexes - perhaps the Detroit equivalent of street corners in Brooklyn. I understand that My Babe by the Supremes is doo-wop but I have not heard it.)
ERROR: Given the 1956 date of that recording and two others on Old Town Doo Wop compilations, the voices, information in the liner notes, that Motown was started in 1959 but the Supremes were not there at the beginning (Barry Gordy told them to finish high school first), and that the Motown Supremes began as the Primettes before their Motown appearance, I now believe My Babe was performed by a completely different group - of male singers.

(FTR, 'babe' or even 'baby' was a common term in those days for one's romantic partner, not a sexist term - the Supremes first hit was 'Baby Baby Where Did Our Love Go'.)

Many doo wop groups are still out there performing, especially in the larger centers where more of them came from and the music was most popular (the NY, PA, and LA areas).

HISTORY

Much popular music evolved from other types, with new elements added. Doo wop's roots are in Rythm & Blues, the "scat" style of jazz, and "big band jump" performances. (But it is Rock and Roll.)

Examples of precursors:
- The Mills Brothers, who used minimal instrumentation.
- Ella Fitzgerald's use of many many nonsense syllables, in the "scat" style of jazz singing,

Tempo covers the spectrum, from slooow (One Summer Night, by the Danleers) to very fast (the tight Morse Code of Love, by the Capris), though up-tempo was more common.

Arrangement & instrumentation runs from "basic" (this is street corner music :-) - to symphony orchestra (Since I Don't Have You, by the Skyliners). (Hey, musical purists, use of symphony orchestra musicians was common in rock and roll - check Motown's productions, for example. (Yes, lush strings don't fit the doo-wop characteristic of not needing much instrumentation - nor the limited space on a street corner - no matter how good the Skyliners are. :-)

So where did the term "doo wop" come from, however you want to spell it and if you care? For pendantry read Gribin and Schiff, otherwise just listen - lots of words over the years sound like doo-wop, including one song in which "dooby do wah" is prominent, what sounds like "doo-wop doo-wah" in the bridge of that 50s RnR classic In The Still Of The Night (though it might be "doo-bop" which is in some songs, not surprisingly), and what sounds like doo-wop in Can We Dance by the Turbans.
The Southern California Doo-Wop society tries to trace its history, noting in particular that the term is in the chorus of the 1954 song "Never" by a Los Angeles group called Carlyle Dundee & The Dundees.

Let's not assume someone did it deliberately the first time - sometimes session artists improvised. (As Martha Reeves recalls doing as backup for an early Marvin Gaye recording, and Keith suspects the Supremes did with that warbling hand-fluttering bit in an early hit you may have seen on the Ed Sullivan TV show - sounds like something that would come from people having a bit of fun in a recording session). Years after the term was used in a song someone started calling the music "doo wop".

When did the music exist?
The Doo Wop Nation web site suggests it began in 1948 with The Orioles "It's Too Soon To Know, and ended with a few records in the summer of 1961 as the vocal group sounds of Motown, Girl Groups, and surf music were coming on strong. (Though others talk of 1954-55 with In The Still Of the Night, coincident with what some claim was the beginning of RnR with Elvis et al. In reality given that all have roots it doesn't make sense to have a sharp dividing line - I suspect people are picking a date when a genre really came to wide attention (Elvis on the Ed Sullivan Show certainly must have done that for RnR. :-). But revivals, reissues etc. soon were available so the sound lives on in the heads of nuts like me. ;-) (One example of a revival is the moving-along Morse Code of Love (aka Baby Come Home to Me), recorded in the 1980s - DJ Jim Parsons said "doesn't it sound like it comes busting out of the 50s?". That's a production that sounds like it was fun to sing, if challenging even for young vocal chords.)

REFERENCES:

The Complete Book of Doo-Wop, by Anthony J. Gribin and Mathew M. Schiff. They get pedantic in some sections, but not overly seriously. (Their earlier book Doo-Wop: The Forgotten Third of Rock 'n' Roll covers some of the same material.) Lots of history, many lists of performances, too much attempted categorization.

The book "Doo-wop: the music, the times, the era" (Stirling Publishing, New York) has brief biographies of many doo-wop groups who enjoyed some performing or recording success, as well as a discussion of the roots, emergence, and decline but ongoing influence of doo-wop (including DJ Bruce Morrow's opinion on why doo-wop per se faded in popularity, and his comment on the impact of the payola mess on less-known performers and regional labels).
A worthwhile book, marred by interspersing the poorly proofed bios with the discussion - I took to ignoring them while reading a section of the discussion through then going back to read the bios.
There’s perhaps too much “culture of the day” in the book, covering major political events and things like suburbs and automats. But I won’t complain about “Cousin Brucie” Morrow’s statement in the bio of Alan Freed, praising Alan Freed for rejecting the common practice of not playing music by black-skinned people on radio stations. “He did what he believed was morally and commercially right, ..As the audience grew, the commercials came, .... The program directors who had shunned music by black artists shrunk away when Freed revealed ....not only did audiences want to hear the music, but it was good for business.” (Red Robinson did something similar in Vancouver B.C. He knew what teenagers wanted - music, and he knew that many of them had money (he simply observed the number of student-driven cars in the parking lot of his school).)
I say that money talks for good. (The story of the deep-south record distributor's reversal when Barnie Ales of Motown reminded him of the profit, told in the TV show "Motown Fortieth Anniversary", is another example.)

Here is a site with some doo-wop info:
Doo Wop Groups
I don't see an explanation of doo-wop I thought was there (it needed editing, but was reasonable). However a few of the links are to clubs who might have information.

This site gives history of the term and the phrase, as well as the music:
So-Cal Doo-Wop Society
(they host performances a few times a year).

Wikipedia articles on Doo-Wop and on the 1961 song "Tonight (Could Be the Night)" give information, including claim that the words first showed up in the chorus of the 1954 song "Never" by a Los Angeles group called Carlyle Dundee & The Dundees.

And the "Doo-wop Nation" web site has much info but needs editing. (May be gone, there is a Doo Wop Nation group on Facebook.)

As well, check my page on RnR categories linked from Keith's Music Page - see bottom of this page.

PS: A story about vocal harmony performances:
A local acapella group led off a Bobby Vee rock and roll concert in Iowa - without instrumentation of course. Later Vee's group did a respectable acapella performance of an early rock and roll hit, except they needed their drummer to keep them on track. (Those performances were not doo-wop, since harmony was in the lead, just good fun - nothing wrong with that! ;-) (It did fit the context of the bare-bones venue - a portable stage in a small rodeo arena beside the cornfields.)

And a simpler one: "Soldier Boy" was sung by the Shirelles in unison throughout it.
Yes, with musicians keeping the tempo.