As with the first game, Borderlands 2 offers the chance to play as one of four different classes from the start. These classes are all different from each other, with different skills and abilities. There is one more class for Borderlands, the Mechromancer, which is scheduled to be released as DLC after the game's official launch.
As you level up with a class, you will earn skill points that can be used to apply to skills in one of three Skill Trees. You won't gain access to any of the Skill Trees until level 5, which is when you'll be able to learn your class' main action skill. Skill Trees have "tiers," which will unlock for every 5 points you put into that Skill Tree, so putting 30 points into one tree will unlock access to the final skill.