Hangar Module [August 29th] - Walk around your starting hangar and view the ships you have purchased. The initial release will only feature the original pledge ships: the Aurora, Hornet, 300i, Constellation, and Freelancer, as well as the Cutlass. There will be some limited customization options and testing of the in-game purchase system. Later builds will feature more ships and more types of hangars, as well as allow you to invite friends to enter your hangar with you and use a Rift DK. Note that you will have to wait for the dogfighting module to fly around in your ships.
Dogfighting Module [December 2013] - Exit the hangar with your ships and engage in dogfights with other players, testing for balance, functionality, performance, player count, etc. CIG's target player count per instance is >~100 players, though that may or may not be realized in this portion of the alpha.
Planetside Module [March 2014] - Travel to the surface of planets to socialize with other players and visit the NPCs, businesses, etc that populate the environments.
Ship Boarding Module [2014] - Board ships and engage in firefights with combatant ship crews.
Squadron 42 Module [Mid 2014] - Branching single player missions (Dark Souls-like online component), in which you enlist in the UEE military in hopes of making it into Squadron 42, a team of the most elite pilots of the UEE military. There isn't a fixed ending to the campaign, you could make it into Squadron 42, you may fail. You may be called back into service later when there are expansions to the campaign story, which is absolutely integrated into the same universe as the multiplayer game, but operates as a separate entity.
Persistent Universe Module [Late 2014] - The primary component of Star Citizen, the PU is the open galaxy for you to explore. You create your own gameplay. One server will host everyone playing the game.
Live Release [Early 2015] - Initial release version available for purchase. Continued support is planned, with updates on a two week cadence delivering new content, progressing the living story of the universe, and improving the game in addition to paid expansion packs to the single player campaign at some points.