Hard to say, but possibly dust spun off by the ceiling fan. Or stirred around in the room and then spun to the wall.
It's the same effect as mud spinning off a bike or car wheel, called the "centripetal force".
Looks like the horizontal stripe is at the same height as the fan's blade peeking through in the picture.
But it could also be the drywall seem at 4ft. You can also see the vertical stud pattern, which suggests it's caused by horizontal air movement due to the fan.
Can you confirm this?
Wipe the walls with a dry cloth or a vacuum with brush. Be careful not to scratch the wall. Don't use water too early, as it could cause staining. Then, after the loose dust is removed, wash with a bit of light soapie water. Most paints can take short exposure to water: just enough to make dirt stick.
If you operate the fans seasonally, wipe the blades before operating them.
Make sure your furnace filter is present and clean.
Keep windows closed on dusty days. This could be outside / street pollution. For fresh air intake on "stuffy" days, use a window intake fan with filter instead of leaving a window open.