Google Tag Manager is a free tool that makes it easy for marketers to add and update website tag. It allows you to quickly and easily update tags and code snippets on your website or mobile app, such as those intended for traffic analysis and marketing optimization.
When used well, this can give useful insights about how visitors use your site so that you can improve their experience while achieving your objectives.
Google Tag Manager (GTM) and Google Analytics are (GA) are different tools provided by Google that can be used separately on your site but also work well together.
This plugin can place the necessary container code snippet into your website so that you do not need to add this manually:
DuracellTomi's Google Tag Manager for WordPress
This article gives describes its functions very well:
How does it work with Google Analytics?
For detailed instructions on how to set up you can read this article:
The guide goes into a lot of detail and will make your eyes roll but if you want to know the depth of the capabilities of the tool, particularly for eCommerce, you might like to set aside the time to read it.
This is Google's own page where you can sign up to use the tool.