In the west, the most common game sold commercially as “Mancala” includes the rules for the Mancala Game of Kalah. Kalah was introduced to the west by William Julius Champion Jr.
Kalah is played on a board of 2 rows x 6 pits. The two scoring pits on each end are used in play. The commercial sets start the game with 4 pebbles in each pit (but you can also start with 3, 5, or 6 pebbles in each pit as variants). If you sow the last pebble onto your side of the board in an empty pit, you capture all of the pebbles on the opponent’s side of the board in the pit opposite of the one you sowed your last pebble into. If you sow your last pebble into your scoring pit, you can take another turn.
One of the most common Mancala games played in Africa is the game of Oware. It has an international organization, "The Oware Society," which sets standards for international tournaments. Oware is generally considered to require more skill than Kalah. Oware is also played on a board of 2 rows x 6 pits, and also starts with 4 pebbles in each pit; Oware can easily be played with the sets sold commercially in the west as "Mancala."