When you curse, you say words you wouldn't want your mother or your priest to hear you saying. A curse can also be wishing something awful on someone, like the witch who puts a curse on Sleeping Beauty.
When you hear "maledizione!" in an Italian opera, somebody's having a curse placed on them. The Italian word tells you just what a curse is — it's a "bad saying" — a really bad saying. Like "May you and all your family have nothing but Brussels sprouts to eat forever and ever!" That would be a curse. As a verb, the act of cursing will lead to getting your mouth washed out with soap.