You can run the pulp through the juicer again to extract more juice from it.
I believe the pulp contains mostly insoluble fiber. This type of fiber tends to upset the digestive systems of people like me who have IBS. Although fiber is touted as being healthy, it is *soluble* fiber that is healthy for everyone; insoluble fiber has drawbacks for many people. This is why I would not be adding it to soups, etc. In my opinion, composting is the best use for it.