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 Victeron at 104.
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.
Since the Update 8.2, you can also increase your magic level by wearing certain pieces of Equipment. There are also other ways to (temporarily) raise your magic level, such as using a Mastermind Potion or by eating a Fried Tropical Terrorbird.