When a player gets four cards of the same kind, then s/he is said to have quads. A hand with, say, 5-5-5-5 or 6-6-6-6 is said to be a quad and can be formed either by the cards held in one’s hands or by combining the hand cards with the community cards on the board.
The unmatched card acts as a kicker but is only required if there is a clash of quads, which can only happen in the case of variations. A quad is quite high on the list of poker hands and comes below the straight flush and above the full house. Therefore, it is effectively the second strongest hand in poker.