The object of the game is for each player (playing a ST:TNG character) to distinguish himself in the task of establishing peace throughout the galaxies (sic). You attain this aim by collecting "Peace Treaties" from alien nations spread throughout six different galaxies.
In the Lieutenant Rules (No Reading Required!), you race about the board collecting treaties. Transporter spaces act as tunnels across the board. The player with the most treaties collected wins.
In the Captain Rules, each player gets one or two (depending on the number of players) photon torpedo cards, used to blast asteroid belts which block access to some planets. Treaties come in two colours, the rarer ones being more valuable. Random event cards complicate matters slightly.