If by economic significance you mean the role played by domestic felines in the modern world in terms of their relationship with the ecosystem and the biological ergonomics that it serves, then a cat like all else in the world is a very important member of our planet. The modern feline that we see in prolific numbers in our households are a domesticated version of their ancestors and are a part of the food chain. Felines have survived through ages and are from the same family as marsupial lions, saber tooth lions to name some extinct ancestors and are related to the modern lions, tigers, leopards and panthers as well. They are agile, keep houses clean of mice and other pests and hence play a very economic role in our societies. Why, there's a whole commercial movement these days that aims to appease the owners of this variety of domesticated pets like commercially canned cat food, and other paraphernalia for it's owners.