Manual:$wgExtendedLoginCookieExpiration

Details
The purpose of this cookie is to allow having a different (usually longer, but this is not enforced) duration for 'keep me logged in' login-related cookies. This means you can e.g. set the standard cookie duration (widely used for MW cookies) to 30 days, but set the 'keep me logged in' duration to a year.

The values mean:
 * null - MW will follow $wgCookieExpiration instead.
 * Positive integer - Duration of 'keep me logged in' sessions, in seconds.
 * 0 - 'Keep me logged in' sessions will last until the browser closes.