No, I didn’t know what it was either. Per Wikipedia:
A fan vault is a form of vault used in the Gothic style, in which the ribs are all of the same curve and spaced equidistantly, in a manner resembling a fan.
This example is at The Unitarian Church of Charleston where I recently stepped in during their open hours.
It was too crowded to get a symmetrical image, but I rather liked this one, showing off the complexity of the design.
The Charleston Earthquake of 1886 destroyed most of the original ceiling along with the church’s tower. Restoration soon returned the ceiling to the 1852 design. Prudently the restoration architect chose a more modest tower which subsequently survived Hurricane Hugo, which in 1989 destroyed many of Charleston’s landmarks.