Bumper plates are a type of olympic weight plate used for olympic lifts where the barbell is dropped frequently. Bumpers are made entirely of high-density rubber, except for a steel collar in the center where it slides onto the bar sleeve.
"Competition" style bumper plates have a much larger piece of steel in the center, more of a core than just a collar that is inserted. Still, competition bumpers have significantly more rubber than rubber coated plates.
Rubber coated plates have only about 1/8" of rubber, give or take. Bumper plates have several inches of rubber to reduce the shock of impact.
Bumper plates are more common nowadays because of the rise of Crossfit and resurgence of olympic weightlifting (the snatch and the clean-and-jerk, the two lifts done at the Olympic Games). Even people doing deadlifts sometimes prefer bumpers because they protect the floor and bar more than iron plates.
For more in-depth information and suggestions, see this article on our blog about bumper plates.