The age old question...first, you keep them species specific...ie, cots with cots, bobs with bobs, scaled with scaled, etc.
They are kept for a multitude of reasons. Some like the individual beauty of each species, some like the song each makes. Buttons or CBBQ can should be kept in pairs and can either be in their own habitat or can be put in the bottom of a cage for other (house type) birds for maintenance, cleaning up the food stuffs that are dropped.
The eggs can be eaten and are actually healthier than chicken eggs, but that is another topic. Some people will blow the eggs out and create art pieces.
There are meat breeds of quail too...cots are good as is bobs...
So you see, they have many reasons for keeping quail....
Why do you ask?