They're not prog, but Coheed and Cambria have some prog metal tendencies. Though, honestly, it only shines through occasionally. Sometimes they're straight up prog, sometimes they're power-pop with a touch of punk or metal (people incorrectly label these songs as "emo," but they simply aren't), and straight up classic rock-inspired songs. So they're not
pure prog by any means, but if you have an open mind and can tolerate Geddy Lee-esque vocals and some songs that are on the poppy side, they're a fun band to get into.
They're considered a "concept band" because each of the albums tell a sci-fi story that continues throughout the course of their discography. I guess the diversity of their sound could have something to do with this, as stories are very rarely epic, brooding, sad, or happy throughout. It's pretty interesting, though more than a little confusing, but it's being told through a series of comics called The Amory Wars (of which 3 issues have already been released). They also have an amazing graphic novel called Good Apollo, I'm Burning Star IV, Vol. 1: From Fear Through the Eyes of Madness, based on the album of the same name. You can read all about that
here and
here.
Their best songs are their "epic" ones though, and the big changes in the story usually happen in these. They're also the ones where their prog influences shine through the most. So if you're really into prog you might just want to listen to those ones (since I know prog fans can be extremely picky and intolerant of things that aren't absolutely
amazing), since certain songs like their radio singles -- which are totally uncharacteristic of their overall sound -- probably won't appeal to you all that much.
Try listening to the song "Welcome Home"
here. If you like that, try downloading the following:
In Keeping Secrets of Silent Earth: 3
Cuts Marked in the March of Men
The Crowing
21:13
The Willing Well I: Fuel for the Feeding End
The Willing Well II: From Fear Through the Eyes of Madness
The Willing Well III: Apollo II: The Telling Truth
The Willing Well IV: The Final Cut