Quirrell is new to Hogwarts. He's the new Defense Against the Dark Arts teacher. And he seems like kind of an oddball. He always wears a turban, he smells funny, and he stutters. He seems too weak and meek to be a threat to anyone, and many of the students consider his presence as Dark Arts instructor a kind of joke.
Underneath that turban, though, is a deep dark secret: Voldemort himself. The Dark Lord is actually living in Quirrell, like a parasite. In opening himself up to Voldemort, Quirrell loses part of himself and becomes a hollowed-out shell. He acts all harmless around the folks at Hogwarts so he can assist his Master in his evil schemes.
While Quirrell acts like a meek, scaredy-cat instructor, as Voldemort he's doing all kinds of nasty things, like killing unicorns. (For more on how Quirrell affects the book's balance between good and evil, check out our theme discussion of "Good vs. Evil.")