To make a sound (used for animals): to cry, call, sing, chirp, or whine (the noises animals make).
朝、庭で小鳥が鳴いている。
In the morning a small bird is chirping in the garden.
夜になると近所の犬がよく鳴く。
When night comes, the neighbor's dog often barks.
子猫が寂しくて鳴いている。
The kitten is crying because it's lonely.
In mahjong: to call a meld (e.g., pung, chow, kong) by claiming discarded tiles.
彼はポンと鳴いて点数を伸ばした。
He called a pung and increased his points.
鳴きすぎると手が遅くなるから注意してね。
Be careful not to call too often in mahjong — your hand can become slow.