Honey is a character from the episode Resignation. She is played by actress Piper Perabo.
Honey accompanied her boyfriend to the clinic because his feces were floating in water. House was amazed that Honey, who is very attractive, was with a boyfriend who was not nearly as attractive as she was. (See No Reason where House notes that both partners of a married couple are roughly equal in attractiveness).
House knew that "floating poop" didn't signify any serious medical condition, but decided to humor the couple in any case. He ran a series of medical tests that confirmed what he suspected - the main reason why poop might float is because someone has been eating a lot of fat. The boyfriend admitted to having a hamburger in violation of Honey's strict vegan lifestyle and they broke up.
House indicated to Honey that he might have an opening for her at the hospital as she was a nutritionist. He talked her into meeting him at a bar after work. She soon realized that House didn't have a job for her and was interested in a relationship. After House admitted all of his faults, Honey was impressed with his honesty, but he admitted that honesty wasn't his strong suit either.