There are four kinds of sets (or basic tile combinations) that can be used to collect a winning hand: Chows, Pairs, Pungs and Kongs.

Chow – a set composed of three sequential Suit tiles
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Pair – a set composed of two identical tiles

Pung – a set composed of three identical tiles

Kong – a set composed of four identical tiles

Normally the winning hand must contain one pair and four sets of Chows, Pungs and/or Kongs. This is called a regular winning hand. Many rules acknowledge also number of irregular winning hands which are not composed of four Chows/Pungs/Kongs and a pair. For more information, see Limit and special hands.

A set that is composed only of tiles received from the Wall is called a concealed tile set. A set that is composed by claiming one of the tiles from another player is called a melded or exposed tile set. A concealed set usually scores more than a melded set.
Note: Some rules consider a melded Kong as a concealed Pung. For more information, see Kongs as concealed sets.

Related topics:
Goal of the game
Regular tiles
Extra tiles
Regular pace of the game
Declaring a melded Kong
Declaring a concealed Kong
Robbing a Kong
Declaring Ready
Going out
Deal ends in a Draw
Faulty declaration of Out