The meteor shower was just like any random shooting stars you might happen to witness on your island. The biggest difference was that it was almost continuous, instead of having large time intervals (20 minutes/30 minutes). Often when Celeste is around patience will be rewarded with a few 'bursts' of falling stars. I spend an entire evening standing on north side of my island waiting for falling stars. It was a clear night and happened to get like 4-5 stars every 30 minutes or so.
During the actual meteor shower I could stand on the cliff and get like 100 stars in less 30 minutes! However, my disappointment was enormous when I found out that only like 40 fragments washed up the next day. My GF who came for the shower too, only got 20 fragments (but finished the achievement from under 50 wishes to start with).
So all in all, a meteor shower is a nice way to get 40 fragments easily, but just paying attention during normal play will also get you quite a few!