When playing Brink the player takes the role of one of four Classes, each of which specializes in various roles on the battlefield. Each Class has a Standard Kit which allows them to complete specific Objectives and perform their battlefield role.
All Classes share the same base statistics (i.e. no Class make you have a faster default running speed) and all Weapons are usable by all Classes. But some weapons are better to use with certain classes, like the Gotlung has low ammo so a Soldier is a good choice for that weapon. Your Class decides what Abilities you can use and what Objectives you are able to attempt.
As you level up in Brink, you earn Level Credits which are used to unlock new Abilities which can be both Class-specific and Universal. Abilities you unlock will further shape what areas your Classes specialize in, but will not change the core skills provided by the Standard Kits.
Generally play as a class that complements your objective sometimes though, play as what you're best as and support your team.