What is 'S' in latin grammar. Singular or something else?

During the holidays the question came up whether the word ‘venison’ was derived the same way as the word for other meats, from the French word for the animal. The answer was ‘sorta’, because it is derived from the old French and Latin words for hunting.

The latin origin was ‘venation’ (hunting) and was followed by an ‘S’ indicating something about the grammar. Does that mean ‘hunting’ singular, and if so, what does the singular of a participial mean? The product of hunting? (i.e. game?)