Can someone explain the origination of the term sniper?

Snipe are wading birds which are sometimes shot for sport, but they are difficult to shoot as they are very elusive, have irregular flying patterns, and usually come to nest in the dusk, when visibility is poor. Plus they live on muddy sea flats and are much the same colour as their environment, and tend to be very wary of any movements in their line of vision.

So, shooting snipe involved a lot of patience, long periods keeping still while waiting for the birds to come into range, plus very fast reactions for the few seconds when the snipe is in view, and Excellent eyesight to be able to distinguish them from their background in poor light.

So someone who made a success of this difficult form of hunting was known as a sniper.

Much the same skills applied to military sharpshooting, and so the name was carried over from hunting.