Cortana is the highly advanced AI at the heart of the Pillar of Autumn. Her design allows her to be uploaded into an appropriately configured battle suit for safekeeping. She is capable of hacking into alien computer systems, and has used this skill to intercept Covenant communications during combat. She interprets this data to provide her caretakers with directional waypoints and the best available information about troop movement and strategy.
Mostly, you're probably going to end up knowing Cortana as "that little voice that tells me where to go." Throughout most of the game, she hangs around your head and supplies you with instructions, for us ham-headed warrior-types who aren't so good at figuring things out. And she plays a pivotal role in the plot of the game.