What bothers Claudius and Gertrude about Hamlet's dress?

A grief-stricken Hamlet is moping around Elsinore, still mourning the death of his father. In keeping with tradition, he is wearing black. Claudius isn't too happy that Hamlet hasn't been able to get over his loss and move on. For one thing, Hamlet's sad demeanor acts as a constant reminder of Claudius's villainous act. Hamlet doesn't know it yet, but his father was murdered by Claudius, and so it's not surprising that Claudius doesn't want to be reminded of this inconvenient fact. He then proceeds to give Hamlet a patronizing lecture, telling him that, although it's awfully sweet of him to show such grief over his father's death, he needs to move on, man up, and start acting like a prince:

Tis sweet and commendable in your nature, Hamlet, / To give these mourning duties to your father: / But, you must know, your father lost a father; / That father lost, lost his, and the survivor bound / In filial obligation for some term To do obsequious sorrow. But to persever / In obstinate condolement is a course / Of impious stubbornness; 'tis unmanly grief (act 1, scene 2).

Gertrude is also a little unnerved by Hamlet's black clothing and equally black demeanor. She too is reminded of her late husband. Though her advice to Hamlet is couched in much gentler, softer language than that of Claudius, her message is pretty much the same:

Good Hamlet, cast thy nighted color off, / And let thine eye look like a friend on Denmark. / Do not forever with thy vailèd lids / Seek for thy noble father in the dust: Thou know’st ’tis common; all that lives must die, / Passing through nature to eternity (act 1, scene 2).