The answer is:
Shakespeare is alerting the audience to the conflict between Claudius and Hamlet.
In Act 1, Scene 2 from "Hamlet," Shakespeare gives the protagonist his first aside as he speaks to Claudius:
Hamlet: [Aside.] A little more than kin, and less than kind.
In his aside, Hamlet, in a play of words, means that Claudius is more than a relative but that he is not kind. Hamlet actually suspects his uncle and father-in-law has murdered his father, King Hamlet.