Basically, what you have right now is a "qualified" student loan (most likely) which you receive a 1098-E for each year, so you can claim/deduct the interest paid on that loan. If you refinance the loan, that basically means you take out a "new" loan and use the proceeds from that new loan to pay off the qualified loan. So the new loan would no longer be a "qualified" student loan, meaning the interest is not deductible.
Now with the interest, that is an itemized deduction that gets claimed on SCH A. until all of your itemized deductions exceed your standard deduction, itemizing your deductions makes absolutely no difference to your tax liability. Therefore, if you did NOT itemize on your 2018 taxes, most likely you will not be itemizing on future tax returns until you have a major change in your financial life that will cause your itemized deductions to actually exceed your standard deduction. For most, that's not gonna happen until you purchase your first home, or you have a financially catastrophic medical situation.
The standard deductions for 2019 are:
single and MFS - $12,350
MFJ - $24,700
Head of Household: $18,350
Now with the current $10K limit on SALT (State and Local Taxes) deductions, for many it will take quite a lot to exceed the standard deduction - especially for a married couple. Take note that if a married couple files MFS, then the SALT deduction each can take is cut in half to $5K each.
