Polonius is portrayed as the well-meaning but prattling busybody who is more apt at giving advice than appying it. As a stock character he is the king's counsellor who has worn out his usefulness but not his tenure. He hangs around, bombastic and obese, puffing out platitudes by the dozen but accomplishing little. (The ladder scene where Hamlet gets an unwanted glimpse of Polonius's hindquarters - depending on the stage directions taken - affords definite comic relief to Hamlet's existential musings.) Nevertheless, he is an endearing father type, sincerely preoccupied with the welfare of his children.
However, when Polonius spies on Hamlet and is mistaken for Claudius, curiousity really does kill the cat as he gets Hamlet's sword tip in the gut and dies from the wound. This accidental murder serves as a catylist in the story line as it puts a rift between Hamlet and Orphelia and Laertes and confirms Hamlet's "madness" (which he has only feigned to approach the truth about his father's murder). Apart from Hamlet's father's assassination by Claudius, it is the first of a long series of bloodshed and murder which leads up to the final dramatic scene of the play.
See the following references for more information concerning the role of Polonius in 'Hamlet':