How do I update the browser on my iMac?

Internet security features continue to evolve and older versions of Safari cannot negotiate secure connections with newer sites.

If you are having trouble connecting to and using websites with your older version of Safari, try it with a newer third party browser that is still being updated to meet current internet security protocols.

If your iMac is of a vintage that precludes upgrading to a macOS version newer than, say, 10.15 Catalina, then I suggest you take a look at Firefox browser or Brave browser. 

To update safari, go to system preferences > software update. If there is one available, click install. For other browsers, update it in the Mac App Store or the website you got it from.