Tucker Tanner is the son of show host Caldwell Tanner and (presumably) Susanna Wolff. Tucker was born as a 14 year old boy, a scientific anomaly which proved extremely uncomfortable for his mother.
As revealed in episode 21, Tucker's tuition and all future debts are fully paid for by the $350 million[1] Caldwell received to convince him to get a full-back "Stay angry, my friends" Angry Birds tattoo, which is believed to be the worst tattoo of all time. It's also revealed that Caldwell bought a house with the money he received (a good one, not a shitty one).