Why the aspect ratio change from 4:3 to 16:9 to even wider formats?

The answer on StackExhange is very good, but misses the history of why 4:3 exists in the first place, which had a great deal to do with mechanical reasons. This is well explained on Wikipedia's entry on the Academy ratio[1].

1: https://en.wikipedia.org/wiki/Academy_ratio

The evolution of aspect ratios---4:3, Cinemascope, Anamorphic, 70mm, etc.---is fascinating. There's a constant trade-off between aesthetic and technical requirements with a lot of really cool innovations for the time.

For my money the most interesting format is anamorphic[2].

2: https://en.wikipedia.org/wiki/Anamorphic_format

It might have some connection with theater sizes. It being easier to widen the screen than to increase the height with the people on a flat plane. Some designed theaters were high as well as wide and were shot with special cameras with people focally seated = IMAX.