Anything that's aching is sore and painful. After a hike up the side of a steep mountain or a long day walking around a city, you'll want to rest your aching feet.
To ache is to feel a dull, constant pain, and aching things ache. Both words stem from the Old English acan, "suffer pain," from a Proto-Indo-European root that might be imitative of a groaning sound, the kind of noise you may make when you have an aching head or an aching tooth. Things are sometimes described as aching in a figurative way, too, when they're full of sorrow, like an aching heart or an aching loneliness.