Emergent Pentecostal here.
It’s not so much a movement as a conversation centered around… well, I think rather than describe it, it’s best just to read some of the authors associated with it: Brian D. McLaren, Rob Bell and Donald E. Miller would be good to start with. And one critic who used to be involved with it is worthwhile too, Mark Driscoll. I’m afraid most other critics just don’t get it.
Actually, to introduce a distinction that’s fairly important to some of us: “Emergent” refers specifically to a group called the Emergent Village, which on the whole is pretty theologically liberal… which is why Driscoll disassociated himself from it. “Emerging church” is a term describing many of us, including Driscoll and myself, who share many ideas with the Emergent Village, but are typically more conservative. If I’m trying to be precise, I’ll call myself an “emerging church” person rather than an Emergent. “Emergent Pentecostal” is a fun sort of oxymoron though, sort of like “Liberal Fundamentalist”.