My apple computer will not let me update Safari

The way Safari is updated is by upgrading your computer's software. An upgrade is when you install a newer version, such as upgrading from Catalina to Big Sur. An update is to install a newer version of the same operating system. The reason for this is because Safari is installed as part of the operating system. It cannot normally be individually installed. Incidentally, a newer version of Safari does not always work with every web site. Sometimes it is necessary to install another browser such as Firefox or Chrome to use with certain web sites. They are individually installed and upgraded.

Safari is part of the MacOS. Just keep your Mac up to date. You're running 10.13, an older OS.