A technique in molecular biology that lets you isolate something, such as your protein of interest (henceforth called the "POI"), from a mixture containing other things.
To do this you need an antibody to your POI. An antibody (aka immunoglobulin) is a protein made by an immune cell called a B lymphocyte, or B-cell, that binds to a specific molecule called an antigen. Usually the anigen is something that is invading your body, but in this case we have injected our POI into a lab rat (or mouse or rabbit) to make it produce lots of antibodies specifically to our POI. (this is the same way that snake antivenin is made). For more information on how to make antibodies and what you can use them for, check out the monoclonal antibody node.
This antibody will only bind to our POI; if all goes well it will not bind any of the other proteins in the mixture. Sometimes, though, it might bind proteins that are very very similar to the POI.
So we have our mixture - it is probably a cell lysate, that is, a soup made of the contents of cells that we chemically ripped open. Our POI is in there somewhere. We add our antibody.
The antibody binds to our POI but not to the other proteins that are floating around. For extra credit we can add something like a Protein-A/sepharose bead (or maybe our antibodies were attached to beads to begin with) so that our POI is attached to this great big heavy thing.
Then we spin down our sample in a centrifuge. As it spins, the largest heaviest things in the tube get sucked down to the bottom and form a pellet, while the smaller, lighter things stay in the liquid which is now called a supernatant (which literally means "swimming on top"). We discard the supernatant and keep the pellet, which now contains just our POI and the antibodies and beads. The POI can be released from the antibodies by boiling with a detergent called SDS.