The wordactually has a Latin deriviative. Cunnis, meaning vagina, and lingus meaning "to lick." So, put it together, you get: to lick puss. Amazing were these words come from. All those things your Latin teacher never taught you.
Excerpt from Merriam-Webster.com showing the correct spelling instead of the incorrect, "Cunninglingus"
Main Entry: cun·ni·lin·gus
Pronunciation: \ˌkə-ni-ˈliŋ-gəs\
Variant(s): also cun·ni·linc·tus \-ˈliŋ(k)-təs\
Function: noun
Etymology: cunnilingus, New Latin, from Latin, one who licks the vulva, from cunnus vulva + lingere to lick; cunnilinctus, New Latin, from Latin cunnus + linctus, act of licking, from lingere — more at lick
Date: 1887
: oral stimulation of the vulva or clitoris