In short, 2K says you can expect a lot of traditional deathmatch gameplay, with players chasing each other and fighting inside the underwater city, separate from the single-player storyline. Maps will apparently be redesigned to cater to a multiplayer experience, and will feature an unlock system many people are used to in modern online shooters. As you progress in multiplayer, you'll be able to customize your character, likely using the same upgrade system the game itself has. They confirmed it will use an experience point system, indicating that a character or at least a profile will stick with you, rather than giving you a clean slate with every game.
As 2K has released more info on the upcoming title, some fans have expressed concern that the multiplayer facet of the game will come at the detriment of the single player experience. That would certainly harm the franchise, which has big dreams. 2K has dispelled those concerns, however, and in fact promises the multiplayer portion will add to the game's overall narrative, with players taking the role of a plasmid test subject for Sinclair Solutions in a prequel-esque setting during the fall of Rapture.