That’s a Southern expression–it means to eat (“gomming down your food”) and talk (“what are you yowing about?”), often at the same time. Not in a talking-with-your-mouth-full kind of way, but eating and talking are two of the most time-honored traditions in my (red) neck of the woods!
As a very Southern gentleman once remarked to me, whilst eating potato salad I’d fixed (made from ingredients I purchased at the closest grocery store in Tarrytown, New York–and they did not have the correct brand of mayonnaise OR pickle relish to which I was accustomed!), that in his opinion, there was “nothing finer than sitting down at one good meal and talking about the next!”
As I said, a true bred-in-the-bone Southern gentleman!