It runs from WordPress's scheduled update checks. Before updating anything it evaluates conditions such as the AUTOMATIC_UPDATER_DISABLED constant, related filters, whether files are writable and whether the directory looks like a version control checkout.

Knowing this class helps when diagnosing why a site missed a security release. If an automatic update did not happen, one of these conditions is usually the reason, and the cause may be a setting someone added years earlier.

Review the relevant settings in wp-config.php and in plugins or must-use plugins, and rely on the official WordPress documentation for the exact behavior of your version.