My 2014 macbook air is on OS X El Capitan and it says I can't update. I'm starting to run in to web sites that won't open... What's the problem?

You should upgrade macOS to the latest version of macOS 11.x Big Sur which is still receiving security updates until about Oct. 2023. Big Sur will also give you access to the latest versions of third party browsers as well. macOS 10.1 El Capitan has not received any updates in years and the Internet has changed a lot in those years which require constant updates to browsers and macOS. Even all the major third party browsers no longer support El Capitan.

macOS 10.15+ no longer supports 32 bit apps so you need to either make sure those apps are updated to 64 bit versions or if no 64 bit versions exist, then uninstall them before upgrading macOS as it will make things easier.

32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

You can find links to various macOS installers within this Apple article which also includes optional instructions for creating a bootable macOS USB installer (you will need at least 35GB of free storage space):

https://support.apple.com/en-us/HT201372

Make sure to have a good backup before attempting to upgrade macOS in case something goes wrong.

You should always have frequent and regular backups. It is impossible to recover accidentally deleted data from an SSD after the Trash has been emptied plus an SSD can fail at any time without any warning signs (even a brand new SSD).