If you have chosen to ignore and update, or just want to make sure you have the latest version of LiveProject, this is for you. Pressing the Check for Updates button will check the LiveProject web site for newer releases than the one you have. If one is found, you will be prompted to upgrade (This window will expand and lead you through the process). You can always go here to check if you have the latest.
Note that new versions are also checked for each time LiveProject starts up, and you may sometimes be forced to do an upgrade. You should generally accept to ensure you have the latest features, bug-fixes, and security updates.
Note that Check for Updates will be disabled if you are no longer eligible for updates.