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 intimated 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.