The idea of Humanity as an integral part of a game system might seem completely alien to some of people, considering there were never rules to represent such a thing in any other game lines. In the early days of roleplaying, the closest you could get to such a thing was probably the sanity system of Call of Cthulhu. When Vampire: the Masquerade released in 1991, it proposed two concepts that were relatively novel to the roleplaying experience. The first of these was that the players were portraying monsters or villains, not heroes or "good guys." The second was that these monsters were thinking, feeling, individuals, capable of being protagonists in their own right.
To better portray the "feeling" part of these concepts, the original creators of the roleplaying game developed the Humanity system. This system acted as a balancer for players, ensuring they had consequences for "evil" or immoral actions. For example, if a player character walked into a restaurant and started murdering people without hesitation, the Humanity system would show that the character is not acting very human, and would therefore make them roll to confront their mental and emotional state in the aftermath of such an action. If any successes were achieved, the character would theoretically feel some level of guilt or remorse for their actions, and would retain their current Humanity rating. If no successes were achieved, this would result in a loss of Humanity, representing the character's Beast slowly destroying what was left of their human nature. What's worse, the loss of Humanity created a sort of slippery slope; the more Humanity your character lost, the easier it was to lose. While the newest system of Vampire takes a different mechanical approach to Humanity, the end result is the same: the player characters are held accountable for the heinous acts they may commit during play.
While its easy to see the Humanity system as a punishment for the power gamers in your chronicle, it can actually be a great tool for roleplaying. In many examples of modern vampire literature, the undead can be seen agonizing over the violent nature of their existence. In the novel Interview With The Vampire, the main character Louis is seen struggling constantly with the idea of drinking human blood and killing humans. Similarly, in the much-maligned Twilight series, the character Edward hates his undead nature, viewing himself as a monster. Even Dracula, arguably the most famous fictional vampire in history, can be seen several times in the novel declaring that he is still capable of love. As a Storyteller, you can use Humanity to encourage your players to develop similar mindsets for their characters.
In a session of Vampire the Masquerade (5th edition) that I recently ran, one of the player characters began the game with a Humanity of 8, putting him slightly above the rest of the coterie. This was a focal point for the genesis of that character, something that he used as "proof" that he wasn't a bad person, even if he did occasionally have to feed from humans to continue existing. When the player failed to control himself during the act of feeding from a teenager on the streets of New Orleans, he drained the boy dry, bloody tears rolling down his face as he was forced to watch the Beast destroy a human life. This scene was perfectly portrayed by the player, who then used the incident to cause a crisis of conscience within the character, changing his fundamental nature and sending him down a very dark path.
Humanity is a great tool that can lead to some really amazing roleplaying opportunities for your players. As a Storyteller, you can even apply Humanity to your NPCs, to shape their actions and motivations. I had an NPC who was the Sheriff of the city in which my long-running chronicle took place, and over the years of that story, he went through a situation where he faced his own moral and ethical quandaries as the player characters looked on, and he ultimately had to resign his post. This was not even a direct consequence of the players' actions, but just a gradual evolution of his character that ultimately saw his story completed.
More than anything else, I would point to the systems of morality within the World of Darkness as evidence that it is not, in fact, "D&D with vampires," as some have insisted. Rather, a game of Vampire offers players the chance to portray thinking, feeling, monsters in an eternal struggle against each other, themselves, and the rest of the world besides. It's a different type of game, my friends. Enjoy it to the fullest.