Magic level is one of your skills.
The higher your magic level is, the higher the damage/healing caused by spells or runes will be. Magic Level does not affect the damage caused by Rods and Wands.
The Tibian with the highest magic level is Averthith Solifitrotus at 100. To raise your magic level you have to cast spells and use mana. There is a spell, called Magic Shield, that makes damage taken by monsters (or possibly players if you play on a PvP-server) not reduce your Hit Points, but your Mana. Mana that is used in this way doesn't count towards your magic level.
There are also other ways to (temporarily) raise your magic level, such as using a Mastermind Potion. Since the 8.2 game update, you can also increase your magic level by wearing certain pieces of Equipment.
Some vocations gain magic levels more quickly than others. Knights advance slowly, paladins a bit faster. Druids and sorcerers advance the fastest. That means they need to use less mana to get a certain magic level than Knights and Paladins.
Hint how to get better magic level. Try to avoid standing in a protection zone because your Magic level wont regenerate there. Don't stand outside depot without carying food Level up by using mana potions