Checking "Remember my Login" will allow your computer to remember your Username and Password from now on so you don't have to Login each time you enter the Member's Community.
In order for this to work, you must have "cookies" enabled. This is usually the default setting for most browsers. If your browser asks you to accept a cookie from this site, be sure to reply Yes.
A "cookie" is a small bit of data that your browser saves and looks up when necessary. Cookies are used by many websites, such as for keeping track of your Shopping Cart when you are shopping at an online store. The member's community uses a cookie to know who you are as you traverse the site. Once you leave the site this cookie expires - UNLESS you check "Remember my Login" above.
Once you are logged into the site, you should Bookmark the member's page, so you don't have to enter through the Public website in order to access the member's area. The Public site usually has information for visitors and seekers, rather than information for members.