Most photographers (prior to digital) learned photography with a 35mm film camera. They learned that certain focal lengths gave them certain angle of views. For example, a lens somewhere around 50mm in focal length gave them a "normal" angle of view (about 40 degrees horizontally). Many mirrorless cameras (Canon M and RF-S, Fujifilm XF, Nikon Z DX, m4/3, Sony E) use sensors that are smaller than the 35mm frame was. Thus, if you use a 50mm lens on these cameras, they show a narrower angle of view. For example, a 50mm lens on the APS-C-sized (1.5x crop) Canon, Fujifilm, Nikon, or Sony (A5xxx, A6xxx) mirrorless cameras would give a 27 degree angle of view. If you divide 40 by 1.5, you get 27 (rounded).
Likewise, if you did want a 40 degree angle of view on those cameras, you'd need a focal length that's 1.5x smaller than 50mm, or about a 35mm lens (again: rounded).
Realistically, the only reason we want to know the crop factor of a camera is to make these angle of view equivalence calculations. If you're not using or didn't learn on other format sized cameras, then you really don't need to know what the crop factor is.
That said, one reason why some get all up-tight about crop factors is that they imply sensor size. Nikon's 2.7x crop sensor (Nikon 1 cameras) is smaller than the m4/3 sensors (2x), which are in turn are smaller than the Canon M/Fujifilm X/Nikon Z DX/Sony A5xxx/6xxx sensors (1.5x), which are smaller than Canon's RF, Nikon's Z FX, and Sony's FE sensors. All else equal—which it never is—a bigger sensor has performance characteristics that a smaller one can't. This is a bit like comparing inline 4 cylinder engines with V6 with V8, though. Yes, the V8 may have some performance characteristics that the 4-cylinder doesn't, but if you're driving normally and no faster than the speed limit, it might not make a practical difference. Indeed, the smaller engine makes for a smaller car and there's an advantage to that.
See also the article on sensor sizes.
See also the article on lens angle of view.
