Yes, dust on the sensor.
Will show up more when:
Big thick pieces of dust
Smaller aperture
Plain background to the dust spots in the image
Most dust instances can be fixed with a photo editing program.
You can clean the sensor, depending on what kind of camera you have. If it isn't an interchangeable lens camera, then you have less luck. If it is you can pay £10s to have it cleaned in a shop, or pay £10s for a sensor cleaning kit. IMO a wet sensor cleaning kit works, but you need two swabs, so a box of 10 swabs will give you 5 cleans.
If you want no dust on your sensor, either get a camera that is sealed or don't change lenses. It's a fact of life.