To use one's own product or service. Originally applied to software companies using their own software in-house, the meaning can extend to any situation that might impose some burden on customers, clientele, constituency, co-workers, etc.
Sen. Chuck Grassley (R-IA) proposed an amendment requiring members of Congress and their staffs to buy health insurance on the exchanges they are setting up, forcing lawmakers to get insurance the same way some of their constituents will. In some circles, this is known as "eating your own dog food."
-- from electoral-vote.com, 14 Oct 2009
A (historical) example of -not- eating your own dog food would be Microsoft developers using IBM's OS/2 operating system while developing Windows software because it was more stable than their own operating system (Windows 3.1 and Windows 95 at the time).