Norton glosses Hamlet's famous line "Conscience doth make cowards of us all" (2.2.85) as "both consciousness (introspective knowledge) and moral conscience." Consider how the alternate meanings and how they differ in analyzing the character of the Prince.
Hamlet's consciousness includes the knowledge he has from the ghost that he was murdered, not passed on by natural causes. He finds himself pulling inward to figure out the right course of action...does he believe the ghost, or hang out a bit longer for more proof? This consideration makes him pause and perhaps fear to act for lack of knowledge he can trust wholeheartedly.
His moral conscience makes him a coward since he can not bring himself to seek revenge when Claudius is praying.
Hamlet wants to do the right thing and is afraid of doing the wrong thing. Ultimately, he's a good guy...maybe too concerned with appearances?