Manual:$wgRememberMe

This configuration parameter allows to show a "remember me" checkbox on the login form (special page "Login") that, when checked, will cause it to take more time for the authenticated session to expire. It can also be configured to always or to never extend the authentication session.

Details
Valid values are constants of the  class:
 * : The user may be able to choose whether to be remembered or not (depends upon whether login form is skipped)
 * : The user will be able to choose whether to be remembered or not (forces login form not to be skipped)
 * : The authenticated session will always be extended
 * : The authenticated session will never be extended