Tag Managers exist to manage all of the third party tags in one centralized place. They have made installing and activating tags much easier. It was a logical and necessary evolution for website management.
What I didn't expect to see, years later, is how Tag Managers would become a multi-purpose asset to a website - an asset that would manage far more than just analytics codes.
There are also dozens of third party integrations that allow for easy implementation of some of the apps you may already be using. This makes setup (and maintenance) that much easier to manage.
Below is the general Google Tag Manager video. If you have any questions about how it works, I'd be happy to help you get started with Google Tag Manager.