Light armor gives you bonus spell power, spell critical chance, magicka regeneration, reduced magicka costs, spell resistance, and spell penetration.
Medium armor gives weapon damage, weapon critical chance, stamina regeneration, reduced stamina costs, increased run speed, and reduced stealth costs.
Heavy armor gives bonuses to physical and magical damage resistance, health, health regeneration, and returns magicka and stamina when you take damage.
If you want to play a healer, you should be running 7 pieces of light armor with all of the perks in the light armor tree. Medium armor is the go-to for melee damage dealers, and heavy is for tanks.