You need clear your cookies to close your session:

• elete cookies to remove the information websites have stored on your computer
• Cookies

Details like websites remembering you (log you in automatically) are stored in a cookie.

• Create a cookie 'allow' exception to keep such cookies, especially in case of secure websites and when cookies expire when Firefox is closed.
• Tools > Options > Privacy > "Use custom settings for history" > Cookies: Exceptions

Let cookies expire when you close Firefox.

• Firefox/Tools > Options > Privacy > "Use custom settings for history" > Cookies: Keep until: "I close Firefox"

Create a cookie 'allow' exception for cookies that you would like to keep and have websites remember you.

• Firefox/Tools > Options > Privacy > "Use custom settings for history" > Cookies: Exceptions