Something magical seems to work by way of some mysterious, unseen force. If you had magical powers, you could make annoying people disappear or instantly fill your room with adorable kittens.
Wizards and witches are know for their magical and sometimes evil powers. However, a gorgeous sunset or a perfect day at Disney World can also feel magical. Magical comes from the Greek magikos, (also "magical"), from magos, "member of the learned and priestly class," probably stemming from the Proto-Indo-European magh-, "to have power."