take a look at this ad for a basketball court stencil...
http://www.ontimecolor.com/cgi-bin/ontimecolor/basketball.html

the rectangular area is usually painted, in ref. to the rest of a wood floor, some highly contrasting color (e.g., one of the school or team colors). this area is the "three-second lane" (from the rule that says you can't camp out in there waiting for the ball to come) or just the "lane"
or "the paint". here's another link showing someone about to "finish in the paint".
http://www.ebasketballcourt.com/