Equipped creature gets +3/+3 and has protection from each color that's not in your commander's color identity.
Equip commander {3}
Equip {5}
If your commander is a card that has no colors in its color identity, Commander’s Plate gives it protection from all colors.
If you have two commanders and attach Commander’s Plate to one, it has protection from each color not in your two commanders’ combined color identity.
If you have no commander, Commander’s Plate grants no protection abilities. The equipped creature still gets +3/+3.