What is and how do you get rid of mold on potting soil of seeds started indoors?

It's mold. Identifying exactly what kind is a job for a biologist specializing in molds; it's not trivial to do.

There are soil fungicides... your local garden center probably has them. Also, it's a good bet you're overwatering; most molds like very damp conditions. If you can set the pot outside in the sun for a bit, that will probably help considerably even without the fungicide.