In a nutshell, front matter is the metadata associated with a given piece of content. This metadata can be in the form of YAML, TOML, or JSON, and is placed at the very top of the content file, between two triple-dashed lines. Here's an example:
title: "My Hugo Site"
date: 2019-04-03T21:45:02+03:00
draft: false
The front matter itself is everything between the triple-dashed lines. As you can see in the example above, the front matter can contain a variety of information, like the title and date of the content, or whether or not the content is a draft.
One of the great things about front matter is that it's completely customizable. You can add whichever fields you want to your front matter, and Hugo will make that data available to you in your templates. This gives you a lot of power to add metadata to your content that can be used to customize your site.
If you want to learn more about front matter, I recommend checking out the Hugo docs on the subject: https://gohugo.io/getting-started/configuration/#front-matter