Carefully means cautiously or painstakingly. If you carefully study your vocabulary words, you'll ace your next quiz!
This adverb comes from the Old English carfullice — but before coming to mean "in a way that avoids harm," it meant "sorrowfully." In fact, the very oldest meaning of care was "to be anxious or to grieve." These days, you don't cry when you do something carefully. You just take your time and make sure you're doing it right and that no one's being harmed by it, like when you check carefully behind your car for the neighbor's cat before you back out of the driveway.