The "Remember me" checkbox allow your login and password you entered to be remembered for future WeBasKet use.
Then, you willn't have to re-enter your login and password for the next year on this computer.
So, you will gain time for each WeBasKet use.
Note: The "Remember me" feature need you to have cookies enabled in you browser (this is often the case).
Your login and password (in its crypted form) are stored on the computer you are logging in (in the browser cookies).
If you are on a public computer, or if other people can access to your computer account, it's generaly advised to not remember your login and password.
Otherwise, everybody could potentialy read your login and your crypted password.
This would allow other people to use your account in your name: view, modify or remove your data and your account.
Even without remembering, connexion is kept active until you close your browser.
If you are on a public computer, then you should close the browser after having used WeBasKet.
In the counter case, when leaving the computer to somebody else this person could continue to use your not-closed connexion.
Those concerns apply when a computer is shared between multiple people.
If you should identify you before using the computer, your computer session is securized and the issues in this page do not concern you: you can remember your connexion (as long as you don't let other people to use your computer session, of course).
WeBasKet Beta, a network tool to share ideas with other people.