Level

Level can refer to many things: a character's overall Character level, individual class level, caster level, spell level, Guild Level, quest level (either actual or equivalent), and minimum level for equipment, among others.

It can also be used as a verb, referring to the process of increasing your character level, as in "Everyone take 10 minutes and level, then we'll continue to the next quest", or "By the end of these quests we should all level to at least 7."

Class Level
Your class level is a measure of how far you have advanced in a particular class. For example, if 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 on character levels.

Caster Level
Your class level in the class you are casting a spell with. See the specific caster level page for details.

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

Spell Level
Spells are also broken into levels based on general strength. Spell levels range from 1 (the weakest) to 9 (the strongest). Only dedicated casting classes have access to nine full levels of spells; the strongest Bard spells are only level 6, and Paladin and Ranger spells stop at level 4. Spell levels do not match character or caster levels one-for-one. It can take two, three, or even four caster levels to gain access to a character's next level of spells.

Guild Level
Guilds (after purchasing a ship) can progress their renown and gain access to new ship buff amenities and then place them on their ship.

Other uses of level
In classic pen and paper D&D, dungeons often have "levels", separated by staircases, ramps, chutes or whatever. The deeper you are in the dungeon the tougher the level of challenges found in that area.