You may have used Google Analytics (GA). You asked your developer to install GA code snippet on your website. And then you have found cool heat map service (or some another service you can’t leave without), and again asked your developer to install code for it. And then it repeated again, and again. GTM manages all these code snippets in one place, so you don't need to disturb your developer.
These code snippets are called tags in Google Tag Manager.
So, Google Tag Manager is a system that allows you to manage tags with user-friendly interface. And it’s done without the need to edit your website every time you want to add or change some code snippet. This makes marketing process more efficient and convenient.