Hi,
It is not the "update" button. It is a "Check for Update" button and was supposed to be linked to here:
www.flexiblewebdesign.com/forum-joomla-virtuemart-template-lightmart-support/969-request-lightmart-update
So, you will see if there is a newer version available.
If there is, then you will download the new version from our server (through "My Account") and install this ZIP file:
One-By One > tmp_flexible_lightmart.zip through Joomla Extension Manager to update the LightMart template.
Regards,
Support