A level is a number that represents a player's overall skill and experience. It has no direct effect on the player character.
The level bar fills up as more mobs are defeated, and once it's full the player is rewarded with an enchantment point. All players in that multiplayer game also restore back to full health.
In a multiplayer game, all players share the same amount of experience. The amount of experience is dependent on the mission's difficulty, rather than the sum total power of all the players. This makes power-leveling effectively possible.
To "level" or "level up" means to gain enough experience to reach the next level. As the difficulty of the game increases, the experience rewarded for overcoming it also increases. As players gain more experience points, the amount of experience needed to level up typically increases. There is no level cap in Minecraft Dungeons [needs testing].
Players earn an enchantment point each time they level up. By salvaging all enchanted items, the number of enchantment points are equivalent to the value of the current level - 1 because you don't get an enchantment point on level 1.
Points are invested in equipment enchanting.