The character is the player in the Infinity universe.
Out of Universe Edit
The character is always in a spaceship, and it is likely that there is both first, second and third person views as seen from demos. As the game is sandbox-style and open-ended, the player is free and not confined to storylines or missions. It is mentioned that the player can explore an entire galaxy, approach or land on every object (most likely planets, gas giants, stations, cities and possibly asteroids). It is unknown what effect going near stars or black holes would cause - whether or not the ship is destroyed (or experiences time dilation near a black hole), although it is speculated that it may be possible to scoop stellar material from stars.
The Character is capable of playing various missions and storylines or living in various roles, whether it be a mecenary role or a scientist role. There is no points to be gained, the skills are actually the learned skills of the player (as in twitch based combat, for instance), however, ranks do exist.
The player makes a name for him or herself in the galaxy.