It's normally applied to new software. The developers show confidence in their new product by actually using it - "eating their own dogfood". Often their management tells them to - and not use (or be seen to use) a competitor's product.

I first heard it years ago when Mozilla employees - Mozilla having been created out of Netscape - declared that their new browser, which was just called 'Mozilla' in those days, was good enough for 'dogfooding'.

An infelicitous word IMO. The must be a better one.