My computer was purchased in 2015 and why can't update the browser? I cannot open important webpages.

No. If you’re really running 10.13 on your iMac, you need to upgrade your software. I believe you can run 12.6.5 but check at https://www.macworld.com/article/673697/what-version-of-macos-can-my-mac-run.html

I think I can explain what might be happening. If you are unable to access certain web sites and possibly getting a message that your browser must be updated, this is not an unusual situation. The reason is that web site providers and software engineers write their software to work based on standardized specifications. Some web sites and older browser software may not be compliant. One thing that may work is to upgrade Safari or you can use another browser that does work such as Firefox or Chrome. They can be individually updated as needed. It is important to know that Safari is installed as part of the operating system and it normally it cannot be individually updated. Safari is typically updated when the computer's operating system (OS) is updated or upgraded. Finally, even if you are able to update Safari, there is no guarantee that it will be compatible with every web site. This is why many of us have more than one browser installed.