I have only wrote about awards from ARBA sanctioned shows. When showing at a fair, they usually have money as awards, and the usual Best of Breed and Best in Show. Some fairs are sanctioned.

Champion Legs
Legs are awarded when one rabbit gets first place, if there is 5 or more in that class AND atleast 3 exhibitors.
Legs are usually also awarded if a rabbit gets BOB and BOS if there is more then 5 in the breed and 3 exhibitors. BIS gets a leg too. No more then one leg can be awarded per show. I will explain what BOB, and the rest of the abbreviations are below.

BOV, BOSV, BOG, BOSG

Best of Varierty (BOV) is the best rabbit in that class of that color. Best Opposite Sex Varierty (BOSV) is the 2nd best, but has to be the opposite in sex of the winner of BOV. The winners of BOV and BOSV stay up on the judging table and are judged for BOB and BOS.

BOB, BOS

BOB (Best of Breed) and BOS (Best Opposite Sex of Breed) are both judged from the winners of BOV and BOSV. So those who win BOV or BOSV stay on the judging table and go up for BOB or BOS. Only one male and one female may win this. So if a buck is chosen as BOB, a doe must be BOS even if there is another buck there, that is a better rabbit then the doe.
The winner of BOB goes up for BIS later on in the show.

BIS, 1st Runner Up, 2nd Runner Up

BIS is the big win. It is Best In Show. All of the rabbits who have won BOB go up for one last contest to see who will win. The judge picks the best rabbit off the table. So one rabbit from every breed will basically go up for this. All the ones who have won BOB anyway.
1st runner up is like second place to BIS. 2nd runner up is like third place to BIS. They also use Best 6 Class or Best 4 Class. I have seen many rabbits win BIS and 1st runner up. Thus winning both places, even though I don't think it is fair, but it's not my right to question a judge.

Points

When a show is sanctioned by a club you are a member of your rabbit will get points for winning certain things. At the end of the year they add up all the points, and award the people in the top 10 usually with prizes. Different clubs may give different points or awards, but I know FSRBA (Florida State Rabbit Breeders Assoc.) awards trophies and some other things. To get these points and for them to count, you must be a member of the club that is sanctioning the show, or running the show.