However the term has been heavily popularised by MTV as a reference to the pop-punk/emo bands of the new century (Finch, Story of the Year etc).
Most modern (post-2000, really) bands referred to as screamo are either emocore, such as Alexisonfire and Thursday, or mall punks wearing eyeliner and trying to be scary, such as The Used and My Chemical Romance. Derision should not be layed against such mall punk bands, however, as they still have enough balls to wreck their vocal chords while singing about how they're just kids and thier lives are nightmares.
"The Used is a great screamo band." INCORRECT
Note : Just because you heard The Used and Finch and thought they were screamo doesn't make them the first ones to do it, and doesn't make it screamo. They are very far from it. I doubt you'll hear Hot Cross or Yaphet Kotto on the radio anytime soon - and that's just the way we like it.