You have pull in the mortal community, whether through wealth, prestige, political office, blackmail or supernatural manipulation. Kindred with high Influence can sway, and in rare cases even control, the political and social processes of human society. Influence represents the sum of your political power in your community, particularly amoung the police and bureaucracy.
Some rolls may require you to use Influence in place of an Ability, particularly when attempting to sway minor bureaucracts. It is, of course, always easier to institute sweeping changes on a local level than a worldwide scale (e.g., having an "abandoned" building demolished is relatively easy, while starting a war is a bit more difficult).
Taken from Vampire: The Masquerade (Revised) P132.