Climbers don't wear gloves while bouldering, sport climbing, or any other type of rock climbing, with the exception of crack climbing in which the climber may wear a special kind of glove that covers the back part of the hand, leaving the palm uncovered.
Climbers don't usually wear gloves because gloves reduce the friction between the climbing holds and the climbers hands. In very easy and beginner level climbing, this may not be so important, but for later on it will be crucial and could prevent climbers from holding certain holds.
Some holds require a large amount of friction, otherwise you can just slip right off. Wearing gloves, even those that cover only the palm and leave the fingers exposed, reduces that much-needed friction way too much. This is also why crack climbing gloves cover only the back side of the hand, and not the palm. Crack climbers still use their fingers and palms for climbing, so they must be exposed and not covered. The back side of their hands are covered up to help reduce pain and injuries from the pressure of their hands against the cracks.
