When you catch them, they look kind of like hairy flies. Though, the white fluff is not hair, but rather a waxy excretion.
When they are flying they look like tiny fairies in the air, thus their nickname - they are also sometimes called "fluff bugs", or even "fuzz-butts".
They only grow wings in the fall (or sometimes in late summer), when they are migrating to the trees where they will lay their eggs for the winter. As I understand it, they are relatively harmless, as aphids go, and are food for many beneficial insects. So, if you run into a bunch, don't worry about "dealing" with them - just enjoy the wonder filled show of these flying, fuzzy, fairies of fall.
It's great to be a homeschooler.