You want to measure what happens on your site: where visitors come from, what they do, whether your campaigns pay off. That requires JavaScript tracking scripts on your site, also known as marketing tags.
Without a tag manager that means: open the code editor, paste the script, adjust it, deploy. Fine for one tag. At ten tags you have a mess nobody can read, and every change needs a developer.
With GTM you paste one snippet into your site once. After that you manage everything through the interface.