Principal Skinner's name is a joking reference to the famous psychologist B. F. Skinner, famous for his theories that with appropriate reward and punishment--conditioning--techniques, any behaviour could be introduced into an individual.
Skinner is the prototypical educational bureaucrat, constantly concerned with a low-grade battle against the school's inadequate resources, largely apathetic teachers, and largely rowdy and unenthusiastic students--Bart being the standout example. Lisa, meanwhile, as the school's genius, is to be exploited to make the school look good, particularly when the district's educational Superintendent Chalmers, whom Skinner fears greatly, is visiting.
Seymour Skinner's personal history, like many Simpsons characters, is somewhat convoluted. It was long known that he was a Vietnam War veteran, single, living alone with his domineering elderly mother. However, in an episode devoted to filling in the character's backstory, it was revealed that he was actually an impostor, having stolen the identity of his platoon sergeant at the end of the war.
In later seasons, he formed a furtive, but seemingly long-term, romantic relationship with Edna Krabappel, one of the exceedingly few cases where Simpsons characters have apparently undergone personal evolution within the show's history.