What does number of forms mean?

I see that, for example, in the free version of your service that there can be "5 forms." If If I am using my forms to be signed, does that mean that I can  have 5 templates or "types" of forms, or does that mean I can only have 5 people ever sign my form?

It refers to the number of forms active on your FREE account. You can see in your My Forms list page the active forms.

The number of forms active per plan level is different.

Check also : Understanding Your Account Usage and Limits

Let us know if you need further assistance.