Others have explained very well already. Here are my 2 cents....
E.g. Let's say some one has 200 points available at $10 each. (That's the average price). You want to go early Dec. A 1-bedroom a week then will cost you exactly 200 points in Beach Club; or 162 pt for a standard view in Boardwalk, or 160 pts in OldKey West.
You contact the renter. You decide you want to go to Boardwalk. S/he calls member services. If the room is available, the renter make reservation on your behalf, you then send her $1620 (162 pt x $10/pt). It's a deal because regular 1 bedroom a week would have cost you a lot more. The ressie will be under your name, and you can call Disney to verify. When I rent points out, I normally have the confirmation send directly to the rentee.
The catch is that the renter may not be able to get the hotel you want to stay. S/he will normally explain to you before she makes teh ressie. Also, there is really no cancellation, because the renter has to commit the points. If you back down, the renter will have to make sure s/he rents the same amount out within the year.
This is a particularly good thing if you wanna try out DVC before you buy. And it's really a deal for Sun-Thurs stay. Weekend points are too high.