This is still being discussed among experts. The simplest answer is: hunting magic. By painting an animal the painter could get a kind of power over it to be used in hunting it.
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Australian Aborigines still produce cave paintings.
The availability of different colored stones allowed the Prehistoric people to create different colors in their cave paintings. Animals were the subject of many of the paintings.
In Europe there are such paintings in some French caves (e.g. Lascaux), in Spain Altamira Cave, in Russia in the Ural mountain caves.
The most likely would be the cave paintings at Lascaux, France.
Rupestrian means inscribed in rock. A fancy term for the rock and cave paintings and carvings left by early civilizations.