Eugene Schwartz was a patient who came to the clinic and complained that he was "squawking". Dr. Cuddy sent him to see doctor House (The reason she sent him to see him was to piss Dr. House off). House told him to give Dr. Cuddy a stool sample.
Cuddy is meeting with wealthy philanthropists when Schwartz walks in with a paper bag containing his stool sample. He adds "Here's my poo!". While House is in the middle of something else later on, he receives a phone call from Eugene Schwartz complaining that he had squawked again House hung up on him. Eugene Schwartz makes one more appearance throughout the episode Both Sides Now when he sees House in the hallway. House initially diagnoses it as acid reflux causing his vocal cords to tense, but when Schwartz adjusts his belt due to soreness, House realizes that he has pancreatic cancer, which was the root cause of the acid reflux.
Schwartz was mainly a source of humor throughout the episode and not an important character.
Schwartz has a wife named Mona.