Linux updating commands

apt-get update downloads the package lists from the repositories and "updates" them to get information on the newest versions of packages and their dependencies. It will do this for all repositories and PPAs. From http://linux.die.net/man/8/apt-get:

Used to re-synchronize the package index files from their sources. The indexes of available packages are fetched from the location(s) specified in /etc/apt/sources.list(5). An update should always be performed before an upgrade or dist-upgrade.

If you are getting the error  

 W: GPG error: http://security.kali.org kali/updates Release: The following signatures were invalid: KEYEXPIRED 1425567400 KEYEXPIRED 1425567400 KEYEXPIRED 1425567400
use following command
 apt-key adv --keyserver hkp://keys.gnupg.net --recv-keys 7D8D0BF6 

apt-get upgrade will fetch new versions of packages existing on the machine if APT knows about these new versions by way of apt-get update.

Used to install the newest versions of all packages currently installed on the system from the sources enumerated in /etc/apt/sources.list(5). Packages currently installed with new versions available are retrieved and upgraded; under no circumstances are currently installed packages removed, nor are packages that are not already installed retrieved and installed. New versions of currently installed packages that cannot be upgraded without changing the install status of another package will be left at their current version. [Emphasis mine] An update must be performed first so that apt-get knows that new versions of packages are available.

apt-get dist-upgrade will do the same job which is done by apt-get upgrade, plus it will also intelligently handle the dependencies, so it might remove obsolete packages or add new ones.

In addition to performing the function of upgrade, this option also intelligently handles changing dependencies with new versions of packages; apt-get has a "smart" conflict resolution system, and it will attempt to upgrade the most important packages at the expense of less important ones, if necessary. The /etc/apt/sources.list(5) file contains a list of locations from which to retrieve desired package files. See also apt_preferences(5) for a mechanism for over-riding the general settings for individual packages.