Hamlet is saying that man must have a purpose beyond mere existence. He speaks on a literal and metaphorical level. There must be more to living than sleeping (which metaphorically he has been doing through his inaction and his failure to avenge his father's murder), or feeding (which is what Claudius has metaphorically done by satisfying his desire for the throne and the queen.)
Hamlet realizes now that he MUST act. Only a beast without the ability to reason would not be moved to action by the events surrounding his father's murder.
Just as the Polish and the Norse armies are willing to die over "an eggshell," he must be willing to risk his life to follow his destiny because he was meant for more than sleep, and HONOR is at stake.