I have received a refund for an order. , and my account says I have a balance of $15. Does this mean I have to spend the money here on Fiverr?
Yes. Your money was returned to you as Fiverr credit; this is like any store credit you would get at a brick-and-mortar store.
You may use your credit to buy any gig of equal or lesser value. If you attempt to buy a gig worth more than your $15 in credit, your Paypal or other primary fund will be charged instead of your credit. This is because there is a processing fee to put money on the site to spend. Your credit has already had that processing fee applied, which is why your processing fee was not returned to you.
This is all outlined in the Terms of Service. You may reference that for a better understanding of Fiverr.