"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")
- progressive entrances of the voices
- a wide range of voices, often including a falsetto voice (sometimes seeming to "float above" the lead) and usually a bass voice, typically punctuating and/or "under" the other singers but not the lead. (We are talking real bass here :-)
- talking through the bridge (the "instrumental" part in the middle)
- or an instrumental solo in the bridge (often a saxaphone)

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; listen for "doo-wop doo-wah" in the bridge)
- 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)
- 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
(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.
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.)

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 and the "doo-wop doo-wah" in the bridge of that 50s RnR classic In The Still Of The Night. 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 later someone started calling the music "doo wop".

REFERENCES:

The Complete Book of Doo-Wop, 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.

Here is a site with some doo-wop info:
Link name to be added
Its explanation of doo-wop needs editing, but is reasonable.

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).

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, but needed the 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 a bare-bones venue - a portable stage in a small rodeo arena beside the cornfields.)