For the average first semester student, these distinctions come up the most in substitution reactions, where hydrogen bonding solvents tend to decrease the reactivity of nucleophiles; polar aprotic solvents, on the other hand, do not.
There are 3 types of solvents commonly encountered: nonpolar, polar aprotic, and polar protic. (There ain’t such a thing as a non-polar protic solvent).
OK, enough yammering. Here are some (hopefully useful) tables.