Here are the level requirements.
Common - 5
Rare - 10
Mighty - 20
Heroic - 30
Epic - 40
Legendary - 50
God - 60
These items can be collected from killing bosses. The Drop Rates of the items depend on tier of the bosses you are fighting.
Many of the these items have socket slots on them in which you can place socket games on them.
You can find the exact stats of the items here.