The meanings overlap. "Quiet" means that there is not much noise. It is the opposite of "noisy." It often refers to non-human noises. "We live on a quiet street," "we camped in a quiet spot and heard nothing but birds and the gurgling river." "Silent" often refers to speech. "You have the right to remain silent." When it is used generally about noise, it refers to an almost complete absence of noise.

I would add that 'quiet' can be a synonym of silent. Many children have been told to 'be quiet.' It means to shut up and be silent.

When talking about sound, silence is NO noise at all, and quiet is very little noise. If you are talking about a person: "She is a quiet person" - she is not loud, does not talk much. You do not say that she is a silent person - this does not make sense because no-one can be silent all the time! If talking about a conversation: She remained silent = she said nothing She stayed quiet = she said nothing OR she said nothing about this topic Hope that helps!

Silent is more extreme than quiet. It means absolutely no noise. If you are in a library, if you speak in a whisper, you can talk quietly. But if you must be silent, you can't talk at all. The city is quiet at night. It wasn't until I left the city until I realised what silent meant.