He is an alter-ego of Patrick who wears doctor's equipment. Nothing he does for SpongeBob actually helps him except plunging up his holes in "Suds."
Role in episode
He tries to cure SpongeBob from the eponymous disease. He tries many unusual methods like spreading Sea-Nut Butter on the soles of SpongeBob's and sandwiching them with slices of bread and persistently ripping a bandage off his face, but nothing he does helps except for plunging up his holes.
SpongeBob goes to Doctor Patrick to help against his splinter. At first, Patrick bizarrely puts SpongeBob's feet in his mouth, not treating the splinter. However, Patrick eventually draws attention to the wood lodged into SpongeBob's thumb after this unusual occurence, though only makes matters worse by hammering it and covering it in garbage, causing his thumb swell up, turn purple, and produce pus.