Chinese carp leaping over the dragon’s gate
The proverb "Chinese carp leaping over the dragon's gate" li3 yu2 tiao4 long2 men
Lengend has it that each Chinese carp would swim up the yellow river upstream to spawn, and those who can leap the waterfall at the dragon’s gate were transformed into dragons.
What does it mean? Simply, if a person works hard at whatever he does, he could one day become successful. This proverb is used to encourage a person to persist in one’s endeavor.
In the past, a carp leaping over the dragon’s gate was used as a metaphor for success in passing the imperial exams.
These exams have their beginnings about 2,000 years ago to select the brightest brains for top government positions.
These exams were open to the public and whoever passes the exams would become a government official, thus ensuring wealth and prestige for the family.
(now you know where the tradition of Asian students taking their studies very seriously comes from.)
Li3 carp sounds like li4 profit so the carp represents advantages, benefits and privileges.
Keeping carp is a symbol of wealth and attracts good luck. Carps are much more expensive than your typical tropical fish, and their market value actually grows as the fish grows larger.
In Japanese, the Chinese carp is called koi.
Here's a nice children's book with a story about the carp jumping over the dragon's gate.