Oh, not as in being single! When you train to become an undine, you're given a pair of gloves to help protect your hands. Rowing a gondola is difficult, especially when you first start out, and you're likely to get blisters. Those trainees are called Pairs. Once you become better at rowing a gondola though, you'll get less blisters and thus won't need so much protection. At that point, if you pass the test to become a Single, one of your gloves is removed, and thus you become a Single.

A Single is what I am. One day though, I want to be a Prima undine, and then I won't have any gloves at all.