Again, I applaud you for asking me instead of typing this query into Google or simply asking your local clergyman for the answer.
Eating out, when not used in a sentence like, “Patty, we have no food in the fridge, let’s eat out,” almost always means oral sex. That is, performing oral sex on a woman. Your confusion is understandable. After all performing oral sex on a woman, going down on a woman, doesn’t resemble “eating out” so much as licking and light sucking. And not even licking and light sucking food! Licking and light sucking vagina.
The term “eating you out” is about as misleading as “blowjob”. Dicks, unless on fire, don’t really need blowing. And vaginas, unless buried in pasta, don’t need to be eaten out.
When said guy said to you “I want to eat you out,” it also implies a certain naughtiness. A certain lusty energy that doesn’t really come across when using the term oral sex. “I want to perform oral sex on you” is something a robot might tell you. “I want to eat you out” is something Jonny Depp might turn and say to you after three cocktails and a stroll along the Seine.
It should also be noted, that if this dude said this to you out of the blue it can be pretty offensive and off putting. It’s a serious come-on and unless you guys have already hooked up or generally talk sexy to each other there is plenty room for you to feel taken back and potentially pissed.