Gyumao is based on Niúmówáng ("Ox-Demon-King", "Ox Devil Lord" or "Ox Tyrant") a character from the Chinese novel Journey to the West.
Despite his threatening name, he is really quite harmless and fun-loving; given that gyū is the crest on his helmet, it is incorrectly assumed by fans that Gyū is his surname and Maō is his first. He was somewhat demonic and frightening when his castle became engulfed in flames on Frypan Mountain. He wreaked havoc through the village at the foot of the mountain, threatening anyone he presumed would steal his treasure, until Kamesen'nin showed him the error of his ways. He is Chichi's father and thus Son Goku's father-in-law. Gyumao is very strong and trained alongside Grandpa Son Gohan under Muten-Rôshi's tutelage.
As the series progresses, Gyūmaō's role lessens in the story and eventually fades into being a background character, used only for slight comic relief. Gyumao is also the grandfather of Gohan and Goten. In anime filler, he has a few large roles though from time to time, mainly accompanying his family and the others.