Cross Materials are the result of monsters being used in a Cross Summon. When a Cross Monster is Summoned, the monsters used for it's Cross Summon are placed in one of the 5 Cross Zones, and become linked to that monster.
Removing a Cross Material from a Cross Monster is referred to as unlinking. If a Cross Monster is removed from the field, it's Cross Materials are sent to the Graveyard.
Cross Materials in your Cross Zone are treated as being on the field, but do not count towards your 5 monster limit.