The game is supposed to be absolutely over the top. You're playing a commando who goes around nuking buildings while standing 30 meters away and yelling "IT'S TIME TO ROCK AND ROLL", and then turns around and instantly shoots 5 people with a single shot from his railgun, and then exclaiming that it was a left handed shot!
Your goals? Depends on your faction.
GDI: Serve the public trust, protect the innocent, and uphold the law. Also kill all dem baddies in Nod.
Nod: PURGE THE MISGUIDED GDI, SHOW THEM THE WAY OF KANE... AND TIBERIUM SANDWICHES FOR ALL.
The easiest way to carry out these goals is to destroy your enemy's base, and killing all his special infantry units with extreme prejudice.