Specifically on the stomach the glp-1 receptors on the vagus nerve increase the stretch sensitivity of the stomach which then translates in lower muscle motility and acid secretion.

In the brain it seems to work both directory in indirectly through neuropeptide y and agouti related peptide. NPY is directly implicated with hunger via increase of agouti and also over expression of y is related to emotional (and physical) pain which a lot of people alleviate by over eating