There are a couple things you can try. First, try uninstalling your google account, restarting the tablet and then readding the account. This may resolve it for you.
Should that not work, then we are sadly at the more serious fix, which is to "Hard Reset" the device. Since this will wipe all data on the device, and make it start over fresh, you may want to try and back up what you can (files, videos, music, contacts, etc. to a computer or other device). You can't back up apps, so that would all be lost.
NOTE: Doing this will clear 'all' the data on your tablet, so it is suggested you not choose this option unless you have to, or aren't worried about losing anything on the device.
Be sure you back up any data you want to keep, to a computer or cloud account, before doing the reset.
To "Hard Reset" the tablet...
1. Make sure that the tablet is actually powered off.
2. Remove your SD card, if there is one in the device.
3. Press the "Power" and the "Volume Up" buttons, together, until you see the start-up logo on the screen.
4. Once you can see the logo, release the buttons and allow the device to enter the "System Recovery Mode".
5. Next use "Volume Down" button to get to the "wipe data/factory reset" option When in recovery mode the "Volume Up" and "Volume Down" buttons are how to can navigate and highlight what option you need.
6. Once you have selected the "wipe data/factory reset", press the "Power" button to select that option.
7. On the following screen, repeatedly press the "Volume Down" button until the "Yes - delete all user data" option is what is selected.
8. Then press the "Power" button to hard reset the tablet.
9. If you took your SD card out in step 2, when the device is up and running again, reinsert the SD card.