What does "Remember my User ID on this computer." mean?
When you sign in with your User ID and password, your browser can "remember" the User ID. Check the box and you won't have to enter the User ID each time you come back.
you will still have to enter your Password each time.

Should I be concerned about security?

Yes, always use 'General' > 'Log Off' in the OSET menu when you've finished working on the website.

If you use a shared computer (in a library, Internet cafe, university, airport or other common area) DO NOT check the "Remember my User ID on this computer." checkbox.

What if I change my mind?
You can always sign out at any time by clicking the 'General' > 'Log Off' button in the OSET menu at the top of each page. Once you've signed out, you can sign in again and choose whether or not your browser should "remember" your User ID information.