Jantou
Jantou「雀」 means the pair in the winning hand. In English, it can be referred to as "the pair" or the eye. Every winning hand requires one jantou. Even the irregular yakuman kokushi musou requires one jantou. Chiitoitsu is a notable yaku, because it requires seven of them.
Fu
Certain tile pairs produces fu. Each produces 2 fu. Any other pair combinations not listed is worth 0 fu.
Essentially, if these tiles were completed by drawing a third or pon was called, then they may qualify for yakuhai, where appropriate.
Tanki
Waiting for:
Only one wait pattern involves the pair directly: tanki. It is conveniently known in English as the "pair wait". This pattern only arises, when the hand contains four complete tile groups.