In sailing, anchoring refers to the act of throwing something heavy into the water, with one end of a rope tied to the heavy thing and the other end tied to your boat.
In economic theory, anchoring refers to the tendency for an initial piece of information to set the terms for future negotiations.
You're selling your 1998 Chevy Malibu. You value the car at $2,000, despite the rip in the back seat and the fact that it smells like a McDonald's Happy Meal. However, the first person who comes out to look at the car offers $1,000. "Uh-oh," you think. "I might not get that two grand." So when a second person offers $1,250, you immediately take it, glad to get the thing off your front lawn.
The anchoring took place with that initial $1,000 offer, making the $1,250 bid look good by comparison. And ya know, Shmoop Premium used to be $1,995 a month - but today can be had for only $24.68 a month! Now who do we appreciate?