Back in the day, most Amiga games were made in Europe, so were tuned for 50Hz refresh, and played 'normally' over here. At 60hz, they would feel wrong, and likewise, US games could feel sluggish and unsatisfying.
Locking the machine to the monitor refresh rate in this way was a curse but also a blessing. It allowed the machines to drive a standard television in various regions, although the image was somewhat blurry, but also the use of dedicated monitors once you started taking it seriously. This reduced the price point and allowed lots of kids to convince their parents to get one :) The higher resolution modes just didn't work out though, so lots of stuff targeted the 320x256 resolution.
The surprise benefit was also that the amiga could genlock to a TV signal and used to overlay onto a video feed, leading to many interesting cheap graphics overlay capabilities which were otherwise totally unobtainable by small TV channels or enthusiasts.
Those were happy days.