The answer is diffraction, and the fact that it takes larger objects to block the longer wavelengths.
1 MHz, which is in the middle of the commercial AM band, has a wavelength of 300 m. In contrast, 100 MHz, which is in the middle of the commercial FM band, has a wavelength of only 3 m.
300 m is large enough so that the waves can diffract around something the size of a typical house, for example. However, the house is much larger than 3 m, so it will largely block 100 MHz signal, assuming it is made of a material that blocks such frequencies. 1 MHz is much more able to "fill in" around house-size objects. At 100 MHz you get a lot more local dead zones and hot spots.
The real difference in propagation distance on the surface of the earth is due to the curvature and roughness of the earth. 300 m waves are able to refract around hills and the general curvature, whereas 3 m waves aren't. The smaller waves are more "line of sight" than the larger ones.
Of course there is still a huge difference between waves used for sight, around 500 nm, than those for commercial FM, around 3 m. The term "line of sight" for 3 m is therefore a bit misleading, the but the effect relative to 300 m waves is quite real. You can still pick up a 100 MHz station even with the antenna being a bit below the horizon while the visible beacon on the top of the antenna is completely blocked. But 3 m waves will get attenuated more quickly than 300 m waves as the transmitter gets further below the horizon.
Bouncing off the ionosphere is NOT the issue in most cases. It is true that 300 m waves can bounce off the ionosphere under the right conditions. This does allow picking up these stations significantly outside their usual broadcast area. However, ionospheric bounce is not why the usual broadcast area is larger in the first place.