In this speech, Claudius is using these body images to expresses the inter-connectedness of Polonius to himself, as King.  This speech comes very early in the play, but we have just recently learned that the late King Hamlet has died and that his brother, Claudius, in now king.  Denmark at this time is an elected monarchy, which means that Claudius is elected to the throne by the lords and courtiers at the royal court. The situation must be a little "political" because this group of people elected Claudius, the brother, rather than Hamlet, the son. Claudius has also just married his former sister-in-law Gertrude. This marriage is usually considered unnatural and inappropriate, but again, something must have occurred "behind the scenes" for the church and the court to go along with it. When you consider both of these untypical events, it becomes clear that Claudius knows how to the play the political game at court to get what he wants.  Polonius is the chief courtier and right hand man to Claudius. In the speech, Claudius is talking to Polonius's son,Laertes, who is seeking royal permission to return to France for school. Normally, it is the courtier who is "kissing up to" the royal family, but in this speech it seems to be almost the opposite. Claudius is telling Laertes and the court that it is Polonius who is vital to the kingdom and the kingship. Just as the head needs the heart, so Claudius needs Polonius.  Just as hands are needed to carry out the actions said by the mouth, so Polonius is necessary to the King. The rest of the line completes the thought.  Claudius says so "the throne of Denmark is to your father."  He means that the throne of Denmark is interconnected to Polonius. This leaves the audience wondering why this connection is so important and who and/or what Polonius is to the king.  This casts some doubts on the character of Claudius in that he would let a non-royal person of his kingdom be that important.