I owe you big time

돕다 is an irregular verb "To help". We use this verb with the grammar 아/어 주다 (To do a favor). So 도와 주다 literally means "To do a favor by helping...." Whereas 도움 is a noun which means "help". 주다 is a verb "To give" or "To offer" So 도움(을) 주다 literally means "To offer help".