Drupal's update hook system is a powerful way of updating your site to introduce things that wouldn't be handled using the configuration system.
Modules will use update hooks to bring sites that have the old version of the module in line with the latest additions to the module. For example, if a new field is added to a table that the module uses then an update hook will be needed to add that field to all sites that are current using the old version. This update hook will be in addition to the install hook that would install the table with the added field in the first place.
There are a number of different reasons why you would want to use update hooks on your own site. Normally being stored in either install profiles or custom modules they would be run on deployment in order to update your dev/stage/production site with changes without having to manually apply them. This is a useful way to do one of the following actions.