taken from pantheon.org
The Japanese goddess of love, eloquence, wisdom, the arts, music, knowledge, good fortune and water. She is the patroness of geishas, dancers, and musicians. Originally she was a sea goddess or water goddess, on whose image many local deities near lakes were based. Later she became a goddess of the rich and was added to the Shichi Fukujin. The island of Enoshima rose up especially to receive her footsteps.
Benten is portrayed as a beautiful woman, riding a dragon while playing on a stringed instrument. She has eight arms and in her hands she holds a sword, a jewel, a bow, an arrow, a wheel, and a key. Her remaining two hands are joined in prayer. It is often related that when a dragon devoured many children, she descended to earth to stop his evil work.
Relevance to Urusei Yatsura
Obviously from the name alone, you can tell that the UY character Benten was based upon this mythological figure. UY's Benten does share a few traits with the goddess Benten, but overall part of the joke of her character is that she's not at all wise, elegant or artistic like the figure she's based on. Rather she's as tomboyish and violent as they come.