After you have enabled the Security Admin, going forward you will be prompted to enter your access key (that you specified when you enabled the option).
From the moment you supply the access key to 'unlock' admin access to the plugin, a countdown timer will begin after which you will be locked-out again.
Any further access to the plugin admin will prompt you to enter your access key.
So, the Security Admin Timeout is how long that countdown timer will last.
Note: This does not apply until you enter the access key again.
To specify the Security Admin Timeout interval, go Shield setting => Security Admin module => Security Admin Settings => Security Admin Timeout and enter how long you want countdown time will last. Default: 30 minutes.
How does the Security Admin Timeout work?
Once the Security Admin session has nearly timed-out, you'll be warned:
This is just a reminder that you should go to your Security Admin settings, and re-enter your access key, If you do not do that, Shield will warn you again and prompt you to reload:
You just click "OK" and Shield will display a new window giving you the opportunity to re-enter your access key:
Note: If you happen to have lost or forgotten your access key, you can disable the feature altogether and delete or re-enter a new access key. Read more here.
For more information about the Security Admin, read the blog article here.