Google Tag Manager (often abbreviated as GTM) allows site operators to dynamically inject scripts or update tracking code without requiring a new deployment. It's often used alongside Google Analytics for the latter.

Others have defined what GTM does pretty well without a basic definition of it's most common purpose. Google Analytics (GA4) has a number of conversions it can track automatically on your website, like if someone spends more than 5 minutes on your site after finding it in search results. GTM allows for customization of certain conversion triggers so you can track more specific actions and those that don't have automatic tracking parameters in GA4. Using GTM just allows for more robust and customizable tracking basically, at least in its most common usage.

Google analytics is loaded by JavaScript. There are also other things like Google analytics that are also loaded by JavaScript.

Updating a website can take time, and usually involves someone with at least a passing knowledge of development.

Google tag manager is a service that lets you embed one JavaScript thing in your page, and then it will handle loading the others. This lets marketing or analytics people add and manage such things without needing to make a full code deployment.
It also lets you make choices about when and how different tracking events for different services are triggered.

It's intended usage is garbage tracking metrics and advertising. Some sites are built more by marketing than developers, and they'll jam functional stuff in there which causes breakage if you block it. These sites are usually garbage though, so nothing of value was lost.