Markup is a system that allows the writer to give basic structure to their text. The most widely known markup language is HTML (Hypertext Markup Language). People can use it to delineate headlines, columns, paragraph text, etc. Markup’s syntax includes tags such as <body>, <div>, <p>, and <em> in HTML, but XML (Extensible Markup Language) is another markup language that has its own discrete tags.
People can use markup to post to blogs and forums if they want to format their content nicely, but this can leave a site open to harmful security attacks if the user uses markup that makes the site link to or load bad content. To solve this problem, a different format of markup was developed so that users could still format text, but in a way that would avoid the possibility of security attacks.
Markdown is a specific markup library, and is one of a few that were developed for this reason. It is used on Github (readmes), Reddit, Stack Overflow, and many more sites. It uses different syntax to achieve many of the same structuring that HTML provides, and is a useful vocabulary to get familiar with.