Some users who have the authority to administer the site might overreact to the scary red messages that show up on the screen if they bump into the admin/logs/updates page or module listing page.
This module adds permission to limit who can see the warnings, who can see the list of modules that need to be updated, and who can change the settings. It's designed to stop pesky inquiries from admins who might misinterpret the update status warnings as critical failures that must be attended to immediately.
Alternative approaches
There are three different approaches to this problem, to be discussed which one to use finally. Afterwards both others should be closed as duplicate:
#2059375: Update notification messages as an option in settings
#3239970: Show update notifications only with permission "administer software updates"
#332796: Add permissions to the update.module to hide warnings (THIS)