Each class offers several class features that give special abilities to your character. For example, rogues can sneak attack enemies when they have combat advantage over them. Fighters have combat challenge, which marks enemies the fighter attacks and makes it difficult for them to move away or attack anyone else. Some class features are required by certain feats.
Some class features can be partially gained through multiclassing. Depending on whether the multiclass feat offers the actual class feature by name, or a similar version (which doesn't count as the class feature), you may or may not qualify for feats that require the feature.