The Chinese character for "fish" is 鱼. This word evolved from ancient pictograms, like the one shown below, which is found one one of those "oracle bones" that the Chinese used to practice divination over three thousand years ago.
In the Qin Dynasty, which unified China in the 3rd century BC, the word took the following form:
The pictograph was eventually standardized to be what it is today, 鱼. As you can see, the four strokes that stand for the tail of the fish were now represented with just one horizontal line.
The character is pronounced [yú].
鱼 is an auspicious word in Chinese. This is because the word sounds the same as the Chinese word for "surplus" or "abundance." It is a Chinese tradition to have a dish of fish on the new year's eve, and the saying associated with this practice is 年年有余 [nián nián yǒu yú] - "year after year there will be surplus." The character for surplus 余 and the character for fish 鱼 are both pronounced [yú].
Fish have been an important ingredient the Chinese diet. This is especially true in South China, where there are more rivers and lakes. A set phrase used to described an area where peasants can make a comfortable living is 鱼米之乡 [yú mǐ zhī xiāng] - "land of fish and rice." This is the Chinese equivalent of "a land of milk and honey."
"Fish are tasty, and so are bear's paws, but you cannot get both of them at the same time." This is an adage from an ancient Chinese philosopher, who was saying that one should not attempt two drastically different tasks. That is, if you try to fish and hunt simultaneously, chance is that you won't accomplish your goal in either effort. The original Chinese expression is 鱼与熊掌，不可兼得 [yú yǔ xióng zhǎng, bù kě jiān dé] - "fish and bear's paw cannot be obtained at the same time."
(Traditional Chinese painting, fish)