Potential energy is stored energy inside the skater, in other words the skater's strength. For example, potential energy is used when the figure skater jumps off of their toe pick. The energy is then turned into a different type of energy.
Potential energy turns into Kinetic after the skater lifts off and they spin on their own in the air. The more potential energy there is, the more kinetic energy there will be. So the figure skater needs a lot of potential energy to be able to get enough kinetic energy to do enough spins in the air.