In it's own way Brink only has the story/Campaign mode.
Off the top of my head I think it's six-ish missions that you play as either the Security or Revolutionaries that follow the main story line and then another three "what if" missions for each side that are more stand alone scenarios. Each of these has an introductory cut-scene from the point of view of your side and then some audio to explain the general misson. There's then a closing cut-scene that shows the outcome of the relevent victors.
If you play through there are settings that allow you to either play with other players or bots. You progress to the next map if you're on the winning team, if you're on the losing team you stay on that map. It's pretty bare-bones but it gives you some options. The bots are useless and playing with them always makes the outcome seem rigged. I'd recommend playing with people as much as possible.
There's also challenges that you do in order to unlock weapons/attachments.
So not a traditional single player campaign a la Call of Duty but there is a story weaved into what the marketing guys called mingle-player.
