Cat drinking milk - Photo copyright pepozzo (Flickr)
Lactose is the sugar in the milk of mammals. Kittens consume lactose as a source of carbohydrates through their mother's milk (colostrum). After weaning the adult cat's diet contains very little lactose.
Most kittens can digest milk. However, some adult cats cannot digest milk and milk byproducts. I don't know the percentage of adult cats that are lactose intolerant. I would presume that your cat is lactose intolerant at least to a certain extent.
Adult cats do not have enough of the enzyme in their digestive system that aids in the digestion of lactose - milk sugars. This enzyme is called "lactase".
The result is that the milk sugars are not digested properly. The undigested lactose passes to the large intestine where is ferments due to the presence of bacteria causing gas, loose stools and diarrhea.
Undigested lactose also holds water in the small intestine. This promotes increased mobility and a large stool.
I don't think small amounts of dairy products are a problem in a cat's diet. Cats like dairy products and small treats are, I believe, perfectly acceptable.
But to put down milk in the time honoured way as has been portrayed in magazine illustrations for decades is unwise. The sensible alternative, albeit pricey, are the commercially available cat milk products.
People have become more aware of lactose intolerance in cats probably thanks to the internet.