When you tick the remember me box the site places a cookie in your explorer temp files, this stays there untill either you delete it of physically click log out. If your worried about security or if your pc is not safe best clean out your history after each session anyway, close IE if thats what you use, click on start then right click on Internet explorer and select Internet properties, then in the middle you will see Browsing history and a delete option click it and now either select what you want to delete or if you are unsure click the delete all.