Because the tax law changes every year, TurboTax has specific versions for each tax year. Right now, TurboTax Online is specific for the 2017 tax year.
If you need to file 2015 and 2016, you will need to purchase and install the desktop version for each year. You can find the prior year versions of TurboTax for Desktop here: TurboTax Prior Year Products. These download installations will allow you to access State returns for the same year.
Unfortunately, the IRS requires you to print, sign, and mail all prior year tax returns (e-filing is not available). But you can e-file your 2017 return now through October 2018.