An ache is a dull, lingering pain. An ache in your calves after your morning jog might mean you didn't stretch enough before you started running.
You might describe your discomfort as a head ache or a stomach ache — in either case, there's a throbbing or continuous pain. A non-physical hurt can also be called an ache, and you can use the word as a verb in either case: "It feels like my heart will ache forever, since my sweet cat died." The Old English root is acan, "to suffer pain," possibly from an imitative Proto-Indo-European word that sounds like a groan.