A smaller sensor sees less of the image circle a lens projects, so it captures a narrower view. Crop factor expresses that narrowing as a single number relative to full frame: APS-C is roughly 1.5x, Micro Four Thirds is 2x, and a 1-inch sensor is about 2.7x.
The arithmetic is straightforward. A 35mm lens on an APS-C body frames like a 52mm lens on full frame. A 25mm lens on Micro Four Thirds frames like a 50mm. This is why equivalent focal length exists as a shorthand — it lets photographers compare across systems without memorising sensor dimensions.
The common confusion is thinking the lens has physically changed. It has not. Focal length is a property of the glass and does not move; only the crop of the projected image changes. Depth of field, however, does shift with sensor size, which is why full equivalence calculations apply the crop factor to aperture as well as focal length.