What is VAT..that's Value Added Tax...for?

After doing my shopping yesterday I thought carefully about which items had VAT added and which didn't.
I did working in a supermarket in the dim and distant past, when items were priced with a pricing gun. White for no VAT items, orange for items that included VAT.
When working on the checkout as well as inputting the price on the tag, you hit the relevant button.
VAT is only supposed to be paid on so called "luxury" items, and indeed one widespread supermarket chain picks up the VAT on a very controversial item......BUT I thought, and remembered from pricing items...pet food has VAT payable on it! Perhaps if a dog/cat/rabbit...(go ahead...substitute the animal of your choice,) was to go in and buy their own food...would it STILL be liable to VAT?
I would love to see my dogs go and buy their own food..and maybe get money knocked off.
Is this VAT fair? Like the other one the supermarket picks up...perhaps it should be questioned....as should several other VAT liable "products"! Who knows?
I would love input.