Title insurance protects the new lender (even if the new lender is the same as the current lender) against any claims against your title since the last policy was issued. These claims could come from contractors that performed work on your home, other lenders claiming a lien against your property, encroachments to property lines or easements from improvements made by you or a neighbor, etc.
In most cases when you refinance, your existing mortgage is paid off and a complete new loan is created. Since the existing lien is being paid off, the new lender wants assurance that their lien will be in first position. Some states offer an abbreviated form of title insurance or a discount on the cost of a policy depending on when the last policy was issued.