Google Tag Manager is part of the Google suite of tools, which is also free. It is easy to use and a useful tool for many marketers. Tag manager enables you to add and update website tags such as conversion tracking, analytics and remarketing options.
When you use tag manager you won't need to keep updating site code which is nice!
Also note that tag manager is not the same as analytics, you can run them without each other but one does not substitute the other.
Google tag manager will make your life a lot easier as you use the interface to fire tags on what page or action you desire.
There are 3 sections to GTM:
Tag: A piece of code that sends information to a third party, such as Google Analytics.
Triggers: These are event driven, when an event is registered by Tag Manager, triggers from the container are evaluated and tags are fired accordingly. No tag can be fired unless an event occurs. An event can be a pageview, a click on a button, a form submission, or any custom event that you define.
Variables: Used to receive or store information to be used by tags and triggers.