Single player and Multiplayer are the same. 2 different sides, Resistance and Security. Objective based, 8vs8, friends or strangers or bots (I think bots fill empty positions, maybe that depends on what game type, single - coop - multi). Friends (And strangers I think) can jump Into a Free position at any time, no waiting till end of match.
Choose any role you want, Solider - Medic - Engineer - Operative. Switch between them at command Posts , Kill ppl, complete objectives, earn EXP etc..
You Can keep up to 16 Characters, Can't switch between them tho, must exit out of multiplayer then select different one (I think).
Good Character/Weapon customization, Different choices depending on Side.
When Creating a Char you choose their side. (It's not random, If you Char is Security you will always be on security team.)
Level Up and unlock more things like body types, abilities etc..
Use that SMART system to get around (Parkour)
Here are some vids showing gameplay, not so much explaining the multiplayer but showing.
EDIT: If you can't find the answers your looking for in the links, Please ask some more specific questions about what you want to know.
Brink @ PAX 10: Bomb Defusal Walkthrough (Cam)
http://www.youtube.com/watch?v=uMn4xZZCBOI - does some talking
8 Mins of gameplay
http://www.youtube.com/watch?v=EfvfIXTFWJc - just gameplay
EDIT: Essentially same gameplay as ^^^ the last link but this is an interview
http://www.gametrailers.com/video/e3-2010-brink/700692 - Some explanation
EDIT: Brink The End of A Genre As We Know It Developer Diary [HD]
http://www.youtube.com/watch?v=dMTynph0QPQ - Kinda gives explanation
EDIT: Another Interview
http://www.youtube.com/watch?v=OLbxAMlNVXE
Im pretty sure there are vids explaining the multiplayer but I have watched too many to remember which ones
EDIT: This is One of the place to see some Brink footage and Dev diaries, Maybe it was one of these that explained multiplayer http://www.gametrailers.com/game/brink/11373