Ballerina dancers typically are very graceful, striving with every movement to embody beauty, flow, grace, and artistic expression. However, in Vonnegut's dystopian future, displaying any of those traits would make those of us who can't dance feel clumsy and bad about ourselves. So, the dancers are burdened with handicaps that keep them from showing any sort of grace or beauty whatsoever. Near the beginning, the story states,
"They were burdened with sashweights and bags of birdshot, and their faces were masked, so that no one, seeing a free and graceful gesture or a pretty face, would feel like something the cat drug in."
So, on their limbs they wore bags filled with heavy birdshot (little pellets of lead) to keep them from moving too quickly or easily; they also had sashweights (like weighted cloth belts) to keep them from jumping too high. Then, they of course had to wear masks, so that any pretty face couldn't show through. Also, if they were too smart, they had mental handicaps similar to the one that Harrison's father, George wore, that emitted loud sounds every once in a while to make any cohesive thinking impossible. The ballerina that becomes Harrison's "empress" has one such mental handicap, along with all of the other previously mentioned ones. Harrison tears them all off of her, and they experience a brief and beautiful dance.
I hope that clarification helps; good luck!