Conquest is all about control. In order to win each team must control a majority of command posts on the map. The longer one team holds a majority the faster the other team's respawn tickets deplete. Once one team is out of respawn tickets they lose the match. Killing enemy players also depletes respawn tickets. Taking all of the command posts and holding them for 30 seconds is another way to win.
Capture the Flag is essentially a big game of keep-away, with deadly weapons. The goal is to bring the flag to the goal zone. In 1-Flag CTF this is a neutral flag somewhere on the map and the goal zone is the enemy team's spawn. In 2-Flag CTF this is the enemy's flag in their spawn and the goal zone is your team's spawn.
Jedi Assault is a large scale epic battle between the forces of good and evil. Light Side heroes and Dark Side heroes must battle until one team reaches the maximum score. That's it, it is a contest of skill in the Force and in your equipment.
Space Assault is all about disabling the enemy capital ship and racking up enough score to win. The enemy capital ship can be disabled either from the outside with starfighters or from within by sabotage. Be warned, the enemy team can repair their interior systems if given the opportunity.
Space CTF is basically just a big version of 1-Flag CTF but in space. Floating somewhere in the void is the flag cannister, pick it up with your fighter and bring it back to your capital ship to score.