downloading an update for my browser. Keep getting a message that my browser is unsupported

Which version of the operating system are you using?

Which browser are you using?

If you are using Safari then make sure all updates from the App Store have been installed. If you are using OS X Lion or earlier upgrade to El Capitan for the latest version of Safari.

Upgrade to OS X El Capitan - Apple Support

Don't blindly jump into El Capitan or any other OS upgrade before ypu know the consequences that go along with the benefits. The important question right now is which OS are you using and exactly which iMac do you have?