This quote by Polonius is applicable to many of the characters in the play -- first, and most notably, Claudius.  The quote means that people who are guilty of something ACT in a way that they hope covers up the reality of their bad behavior.  Claudius ACTS like a devoted father to Hamlet, but he is responsible for Hamlet's father's death.  Claudius ACTS like he is greatly grieved by his dear brother's death when he speaks to the court in Act 1, but again, he is the one who killed his brother.  Claudius ACTS like a devoted husband to Gertrude, but he doesn't love her enough to reveal the truth about the poisoned cup of wine, and he allows her to drink it rather than draw attention to his evil plot against Hamlet.

The theme of ACTING is prevelant throughout the play.  The actors arrive to put on a play and ACT the parts of a king and queen, but it is only a story.  Hamlet is struck by how "true" their presentation seems, even though it didn't happen to them as people.

Hamlet is ACTING crazy in order to distract and lower the guard of the people of the court, especially Claudius.  He hopes that Claudius will reveal the truth of the murder of King Hamlet.

Rosencrantz and Guildenstern ACT like friends to Hamlet in order to try to help him over this difficult time, but they are actually only doing this in order to curry the King's favor in the hopes of a reward.

Polonius ACTS like he is concerned about Hamlet's madness, but is really only concerned with proving his intelligence and worth in discovering the cause of Hamlet's madness (even though we know he is wrong).

The theme of acting and artifice in behavior is a theme that runs through the entire play.  A careful consideration of all of the characters would reveal many more examples.  The above list can you started!