Another word for extortion/blackmail, or the obtaining of a good or service through means of force, threats/intimidation, or abuse of power.
The Mafia would usually give small business owners "the shakedown," in which if the owner did not pay protection money (or "tribute") to the Mafia Don, their store would mysteriously be firebombed by vandals (read: Mafia thugs) who presumably would have been deterred if the owner had opted to partake in the Mafia protection plan.
Shakedown by abuse of power:
City councils are notorious for shakedowns by abuse of power. Suppose you bought a house for an inflated price of $50000, before property values started declining. The state wants to build a highway, and decides that your house is in the way. You don't want to move, but they offer you $25000 to pack up and leave. If you don't leave, the council will employ the eminent domain laws, which will simply *force* you to leave and *force* you to accept a measly compensation of $15000 (fair market value) for your property. While such practice is actually legal, it's still a shakedown, because if you don't agree to their initial unreasonable demands, you're going to be even worse off as a consequence--just like debating whether you want to drown in your own piss, or someone else's.
Head #2: "It's way over there by that old school bus, man."
Head #1: "Right on, you have any extra's?"