What is emo? Those three letters keep popping up here.
To elaborate on Alcon's last paragraph:
In 1984, the hardcore punk scene in DC (and to some extent Maryland), began to have many bands taking a new turn, slowing down, being more melodic, and often changing the lyrics from fiercely political to rather more personal. These bands were often mocked by the rest of the scene and referred to as "emocore", a joking and at the time perjative term which was short of "emotional hardcore." By the late 80s, the sound had spread outside of the DC area and had developed a new identity, not sounding much like hardcore punk at all anymore. Bands began to shift in an even more melodic direction, taking elements of popular indie rock bands at the time such as Slint as well.
In the early 90s, a new variation on the sound took off as well, essentially to "emo", what "hardcore punk" was to "punk". The sound of the mid-phase emo bands was preserved, but made harder and faster. This style was mostly confined to San Diego and to a lesser extent the Bay Area however. The style largely fizzled out in the US around '93 or so whereabouts, but before that picked up big time in Canada (especially Quebec), where it lasted till approximately '95. There it died out pretty much everywhere.
Before this happened though in 93-94 many bands began to play a new style of indie rock heavily influenced by the emo of the early 90s of the non-hardcore variety, essentially "post-emo indie rock". This style was in a sort of ironic twist popular pretty much everywhere EXCEPT the coasts with the notable exception of Seattle. This is roughly about the time the term "emo" began to enter the mainstream.
A bit later around '97, a somewhat revival of late 80s/early 90s emo sound began, based mostly in New Jersey and NYC, South Dakota (yes, I'm 100% serious), northern Florida and Indianapolis (though this happened a bit later). This was a small revival and never hit the big time, and many of the bands became far more popular long AFTER their breakups, with records that now fetch big bucks on eBay. This somewhat amusingly was mostly a result of Napster and the internet introducing these bands to people who would've otherwise never heard them (including yours truly.) By the turn of the century the style was kicking again and big time, but by around 2003 it began a massive slowdown, mostly due to the derivativeness of the bands (rip off after rip off after rip off.) This is pretty much what later became labeled "screamo" by the way. It's still around in the US but probably at a level comparable to the latter half of the 90s rather than the turn of the decades. However about the time it slowed down in the US, it massively picked up in Europe, and is currently huge there (especially France and Italy.)
Meanwhile the aforementioned "post-emo indie rock" style never really made it out of the 20th century in its pure form, but many bands of the scene or spawned from the scene began to play a more mainstream and radio-friendly style of it around the turn of the century, and also began to achieve mainstream success. This is what made the term go mainstream, but since no one in the mainstream had heard of any of pioneering bands, they began to slap the label on whiny mainstream tripe like My Chemical Romance (who were really just the first band of the sound to hit it big), and thus spawned legions of stupid 15-year olds who started dressing just like My Chemical Romance. The result was basically the term being used by clueless mainstream folks to refer to a retarded fashion style, but as pointed out before this is an extreme bastardization as the term and style were in existence 20 years before said retarded fashion style came into existence, and will continue to exist after all people dressing in that retarded fashion style grow out of it/finally kill themselves.