Fan Worm is the same as feather duster, just smaller. The tube is hardened calcium carbonate. The color of the fan usually is white with pink dot, it can also be red or black.
The White fan worm is the most common fan worm and it propagate fast in your tank. It will grow on any rocks. The appear of fan worms indicated your tank has matured. These fan-worms are filter feeder. They are beneficial for the tank besides they look cool.