Level

Your level can refer to many things, either your class level your character level or also spell level or even dungeon level.

Class level
Your class level is a measure of how far you have advanced in that particluar class. For example of you were a 10th level Barbarian and a 6th level fighter then you would have 10 class levels in barbarian and 6 class levels in fighter.

Character Level
Character level refers to the sum of your class levels. In the above example you would have a character level of 16. This is important in determining feats and also ability score increases as they are based off of character levels.

Experience Points
To advance your level, you need to gain experience points from doing quests. Progression table is here.

Spell Level
Spell level refers to different powered spells. Spell levels range from level 0 (cantrips and osirons) to level 9 the highest spell level cast. For example fireball is a level 3 wizard/sorcerer spell, while Cure Light Wounds is a level 1 cleric spell.

Other uses of level
Dungeons are usually grouped into levels separated by staircases. The deeper you are in the dungeon the tougher the monsters are going to be.

A humorous take on all of the confusion can be found here: