Let's face it: Despite all efforts to the contrary, a vampire is going to succumb to moral failure sooner or later in his unlife. Willfully or otherwise (ethics are particularly hard to maintain in frenzy), a vampire occasionally commits atrocity and risks losing his Humanity to the Beast. If the character feels remorse for his actions, he knows that his Humanity is still intact. If he commits a wrongful act and callously disregards it, however, his Humanity is obviously waning.
One of the most important themes of Vampire: The Masquerade is the Kindred's struggle to retain their souls and avoid the clutches of the Beast. Thus, it is extremely important to use morality and Humanity in a consistent, dramatic manner. If the Storyteller allows the players to (sometimes literally) get away with murder, the story will suffer, as one of the tragedies of vampiric existence vanishes. If the Storyteller is too strict with Humanity rules, though, all the characters will be ravening, blood-gorged maniacs by the end of the first session. Keeping a handle on Humanity is a hard thing to do, but the Degeneration system is designed to help that.
The system is simple: Whenever a character takes an action that the Storyteller decides is morally questionable, the character may suffer degeneration - a permanent loss of Humanity. If degeneration is a possibility, the player whose character commits the act should make a Conscience roll for that character. The difficulty is 8 - reprehensible acts are hard to justify - though the Storyteller may modify this. Willpower may not be spent for an automatic success on this roll - all the ego in the world won't protect a character from guilt.
If the player makes the roll with even one success, the character loses no Humanity - he feels enough remorse or somehow manages to justify his transgression. If he fails the roll, the character loses a point of Humanity. If the player botches, the character loses a point of both Humanity and Conscience, and also gains a derangement, decided upon by the Storyteller (who should make it appropriate). Obviously, morality is not something a Kindred can afford to take lightly. Remember that a vampire whose Humanity drops to zero is no longer suitable to be a player's character. (To be perfectly honest, Kindred with low Humanity scores aren't particularly appropriate either, but can be enjoyably tragic figures in comparison to their nobler counterparts.)