Act Three of Hamlet is the climatic act of the play in it, there are many important scenes and conversations. In those conversations the characters speak in metaphors, and some of these metaphors could be seen to have symbolic significance. Here are a few examples:
1. Symbol: Nunnery
Hamlet tells Ophelia to get herself to a nunnery -- a place away from sinful men. He specifically tells her "what should such fellows as I do crawling between heaven and earth? We are arrant knaves all. Believe none of us. Go thy ways to a nunnery." He could literally mean this advice, but at the minimum he is using the nunnery as a symbol of a place where men are excluded, and therefore women are kept pure.
2. Symbol: a pipe/recorder
Hamlet literally grabs a recorder from one of the players and then confronts Rosencrantz and Guildenstern with it, asking Guildenstern to play him a tune on it. When Guildenstern says he can't, Hamlet makes fun of him saying that playing a recorder is "as easy as lying. Govern these ventages with your fingers and thumb . . . [and it will] make eloquent music." When Guildenstern insists he has no skill with it, Hamlet brilliantly turns around and essentially says 'what makes you think you can "play" me? You may think I am a simple instrument but "yet you cannot play upon me" (make me tell anything I don't want to tell). The recorder is a symbol of Hamlet and his revealing his true ideas -- they will never get the better of him.
3. Symbol: Mighty Wheel
Rosencrantz compares the King to a mighty wheel. He suggests that the wheel is the symbol of a king "fix'd on the summit of the highest mount /To whose huge spokes ten thousand lesser things / Are motised and adjoin'd; which, when it falls, each small annexment, petty consquence / Attends the boisterous ruin." If the King falls, he brings with himself all the lesser people of the kingdom because the king IS the kingdom. If the king comes down a hill there will be a large path of destructioin in his wake.