To understand how Composer manages Drupal dependencies, see Using Composer with Drupal. To decide if Composer is a sensible way to update, compare the available options.
For convenience, these instructions include the Drush commands necessary to complete an update: many people find Drush quicker and easier than the web-based admin area.
If this is an existing Drupal site, where Composer has never been used before, make sure it’s ready for Composer first.
With Drupal 9 updating core with Composer is the way to go.