What does he mean?

what he means is, he wants to know if you can be faithful WHILE he gets over what you did.
if you cheat on him again while you both are apart.he'll know you don't love him.and that's it!
my advise, be on your best behavior till he cools off!

Some guys might, but I really don't know in this situation.
The one thing I do know for sure is that you violated his trust, drunk or not, and it will take a long time for you to earn that trust back. Is he the kind of guy who believes "once a cheater, always a cheater"? If he is, or even if he isn't, he still needs time to cope with the violation of trust. You are lucky enough that he does seem to want to pursue a future with you, so don't violate his trust in you again or else you're finished. Give him the time he needs and just be there if he asks you to be.

OOOo bad move. If I was in his shoes, I would definitely walk away from the relationship. If he's anything like me, looks like things are about to be done.

sometimes, I think he just needs time to think about it and get over it, in the meantime I wouldn't hook up wit anyone AND I would still try to go out with him as "friends"

Every time I get told that they just want to take a break I always find that they hook up with other girls then come back when they feel like it. I always take it as an automatic breakup. But You never know. He might be different. Just don't get your hopes up if he doesn't come back yah know?
Good luck