In this second scene of the play, King Claudius greets young Hamlet in a family manner; however, Hamlet, upset that his mother has so quickly married again (and to his uncle no less!) snaps back "A little more than kin, and less than kind!"
This short quip is Hamlet pointing out that the two of them are a little more than just related now and further more he does not see Claudius as being too kind to him. Claudius seems to move past this statement believing that Hamlet is just still upset about his father's death. Instead, he asks Hamlet to take away the clouds that hang on him and to move past this mourning period.
the "and less than kind!" also refers to how unnatural Claudius and Hamlet's relationship is