Silence is quietness, or a lack of sound. When you silence a noisy movie-goer, you shush her.
When there's silence, nothing is heard. Silence is empty, the opposite of a noisy racket. A library is one place where there's supposed to be silence so people can concentrate. To silence someone is to hush him up or tell him to be quiet. Silence also has a more disturbing meaning: if someone threatens you to keep you from saying something, she's trying to silence you. Censorship silences free speech.