Dating can include many happy memories, as well as colorful horror stories. Sometimes dating progresses naturally without any question which direction it is leading. Other times it can be filled with gray areas that may appear to be confusing for one or both of the people involved. Defining exclusivity seems to be one of these areas where the two minds may not come to the same conclusion at the same time. There are a few things you can do to help clear things up a bit.
Ask him. This is the easiest way to find out what you want to know. It can be as direct as "Are we dating exclusively?" or it can be a bit more subtle like, "You're amazing, I bet you have lots of women fighting at the chance to win you over." If he seems a bit confused by the latter or if he directly says he only cares for you, you are in a good position. If he feeds into an ego-based attitude and agrees with the plentiful women he is surrounded by, you may not be the only one in his life.
Evaluate your time together and how it is spent. If the time revolves around sex and you only hear from him once in a while for that purpose, you are lacking depth in the relationship. If you two are enjoying each other's company doing several different things, whether it ends in sex or not, may indicate that the relationship is growing into something more.
Observe his behavior toward you. Calling or texting frequently, making plans in advance, setting aside time for the two of you to spend time together, or doing thoughtful things for you shows that he is spending time and effort on ways to make you happy. This indicates someone who thinks the relationship is worth the effort and is beyond just another meaningless date.
Ask him if he is still using a dating service if that is how the two of you met. A person in an exclusive relationship doesn't need a means to look elsewhere.
Go with your gut feeling. Ask yourself what your intuition is telling you. There is a lot to be said for listening to it and what it has to say in this kind of situation. If it doesn't feel right, talk to him about it or move on with life holding the intention of getting the relationship that you want and deserve.