Authentication problem is a wrong password on a WiFi issue. Nothing huge, just that. So either you are trying to use the right password, but on the wrong connection, or you are using the wrong password on the right connection.
Go into the "Settings" and then "WiFi" and have it 'forget' yours. Then restart (turn off and back on) the tablet. While it restarts 'confirm' your WiFi's name and password. Once it has fully restarted, then go back on the WiFi, locate the correct WiFi name and try to log in. You may also want to turn on the ability to 'see' the password as you type it that way you can be sure you are doing it correctly. And also be sure about any upper/lowercase requirements.