When you subvert something, your words or actions criticize or undermine the usual way of doing something or common values. The girl who wears a tuxedo to the prom might subvert traditional ideas about beauty.
To subvert an institution like a school or a government is to overthrow it or stop its normal way of functioning. Subvert comes from the Latin word subvertere, which combines the prefix sub, under, and the suffix vertere, to turn. So you can imagine something that subverts as overturning or flipping the usual way of doing things, like a student who subverts a teacher's authority, causing chaos in the classroom.