棋 (Qi2) is a Chinese character that forms the second half of the Chinese term for Go: weiqi.
The word 棋 generally refers to "board games", and is used for weiqi, but also xiangqi (chinese chess) and other board games of skill such as Western chess.
Nowadays there is only one way to write it: 棋. At some point in history, another variant was used, which was imported by the Japanese to form the word go: 碁. The two characters both have the same phonetic component (其), but different radicals (or "meaning components"). The standard one uses the radical for wood, while the ancient / Japanese one uses the radical for stone.
In either case, the meaning of the character is the same. The Japanese also use the character 棋 (pronounced ki or gi) for board games other than go, for example in the word shogi.
Note: 气 (Qi4) means liberty.