A stop is a measurement of light. Each stop up is twice as much light, each stop down is half as much light.
Changing the aperture from f/4 to f/5.6 decreases the amount of light to the sensor when the shutter is release by half. Changing the aperture from f/4 to f/2.8 doubles the amount of light to the sensor when the shutter is released. Shutter speed and ISO are pretty easy to do the math on (an ISO 100 lets in half as much light as ISO 800, a shutter speed of 1/100 lets in twice as much light as a shutter speed of 1/200) but with aperture numbers involve square roots and all sorts of fun (you can read about it in many places), so it's usually just easier to remember the scale (f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22...).
It doesn't necessarily mean aperture, though. Often you'll hear talk about stopping up or down studio lights, or certain filters will modify light in stops without adjusting the aperture, or you'll hear talk about using exposure bias to stop up or down. Exposure bias will adjust aperture, shutter speed or both depending on what mode you're in (do any adjust ISO this way? I've no idea.)
Most cameras will allow you to adjust it in half or third stops (some may do others? I'm not sure), many studio lights have smooth adjustments or 1/10th adjustments.