Me and my boyfriend are committed.What does that mean.Does the mean we are in a sex relationship

No not at all. It means you only date him and he only dates you.

Committed means you are exclusive to one another and you do not date others.

Oh so committed means that he's only in a relationship with me and I'm only in a relationship with him?

You got it!

I agree that a committed relationship should mean an exclusive relationship, but I think the term "committed" should also encompass values such as trust, loyalty and caring. If you're in an exclusive relationship but lacking some of those qualities for each other, then commitment isn't present.