Personal exemptions is a tax term. Roughly speaking, there is one personal exemption per person on a tax return. For each personal exemption, you can exclude roughly $4,000 of earned income from federal income tax.
Do you have a copy of your 2015 tax return? If so, just look at the number in the box on line 6d - that is the total number of exemptions you claimed in 2015.
Generally, you can claim one exemption for yourself as long as nobody else (usually your parents) can claim you as a dependent. And you can claim one exemption for each of your own dependents (usually your children). You would claim yourself on line 6a and your dependent on line 6c. If you were married, you could also count a personal exemption for your spouse.
If your situation has changed (for example, if you were a dependent of your parents in 2015 and are not now, or if the dependent you have now was not born yet or was not your dependent in 2015), then you probably want to talk with the financial aid office of the school you're going to about the changes in your situation. You should still fill out the FAFSA based on your 2015 tax information, but if the financial aid office gets additional information you may get a better aid package.