GTM is an acroymn you may have seen if you've been reading about managing or marketing a website. GTM stands for Google Tag Manager and is Google's offering to help website users and marketers manage site tags without necessarily needing to get a developer involved. You can think of it as a bridge between marketers and developers.
Developers include the GTM code on websites and marketers then manage Google and all other third-party tags through the Google Tag Manager interface. Website owners tend to benefit from this structure as whenever the next Facebook Pixel comes on the scene, they can very likely get on board without needing to interrupt (or poke) their developer.
GTM allows for the creation of workspaces and environments that ensure that relevant tags can be created and managed by different teams in an organization and for the appropriate environments. Of course if you run a small business or a solo shop and are not looking for every bell and whistle you can use GTM for old favorites you would expect such as Analyitics.
Variables inside of triggers are used to identify when any one tag or other should be fired off. Variables within tags are used to capture dynamic values about the page. The GTM Overview video below does a good job of describing the basics.
The top level of the GTM Account is your Google account. Once logged in under your account you will have multiple accounts - one for each client or customner. Each Account may have multiple containers whcih contain tags, triggers and variables. Generally speaking the containers each represent a website or (one could be development, another testing, and a third container for your live environment).
If you are not currently using GTM the overhead might not be worth the switch, but if you find yourself constantly tweaking your on-site tags for marketing purposes, Google Tag Manager is a great resource.