Professor Popov is the Russian dancing teacher of the Royal Preparatory Academy, having held this position for many years, as King Roland II used to be one of his students.
When Sofia first attends his class, Amber shoves her forward, which Popov takes as Sofia volunteering. At first things go smoothly, but then Sofia starts dancing out of control (due to magic shoes Amber gave her), ruining the dance lesson.
In the episode "Make Way for Miss Nettle", we learn that he stays late after school and hates evil fairies. When he tried to stop Miss Nettle from finding the Headmistrisses' spellbook, she traps him in a bubble. After stopping Miss Nettle, Sofia, James, and Desmond realize that they had forgotten about Professor Popov, who is still in a bubble. Unfortunately, the bubble began floating around, forcing the children to go after the departing professor. James boasts of Popov's skill as a dance teacher to Sofia, saying that one lesson from him will teach her the ropes. Popov himself is affected by this boasting in him facing Nettle unarmed. However, Roland did not pay attention in dance class, despite Popov's entertaining and forceful personality, and so became a bad dancer, stepping on Sofia's foot at her first ball.
"Popov" (Попов) is a common Russian and Bulgarian surname, meaning "son of the priest".