The new 4-player co-op missions take place outside of the single-player game, and aren't affected by your Mass Effect 1 or 2 saves. "Players can choose from a variety of classes and races, form an elite Special Forces squad, and combine their weapons, powers and abilities to devastating effect as they fight together to liberate key territories from enemy control." The multiplayer does tie into your single-player game in unspecified ways, offering "an alternative method" of achieving success in the main storyline.
The co-op is one aspect of something called "Galaxy at War," a rather mysterious, and optional, system that uses multiple factors (including multiplayer) to augment Shepard's "Galactic Readiness" level. "Other platforms and interfaces will be announced in the coming months," BioWare said, also noting that it will be possible to obtain the "optimal" ending without doing anything in the Galaxy at War mode.
Whatever it is, we're Galactically Ready to find out more.