In more detail
Created by John Gruber in 2004, it is used for README files, documentation, forums and note apps because the source stays readable. Several flavours exist, such as GitHub Flavored Markdown, which add tables, task lists and strikethrough. The original description left edge cases open, so the CommonMark specification (2014) pinned down exactly how each construct is parsed, and most modern flavours build on it. A converter turns Markdown into HTML; the symbols are a shorthand for tags.
Why it matters
Because the result is just text, Markdown is easy to store in version control, diff, search and move between tools, unlike a word-processor file. The catch is that flavours differ: a table or footnote that works on one site may print as plain symbols on another, and line breaks, nested lists and underscores inside words are common sources of surprise. Most renderers also allow raw HTML inside Markdown, so output built from untrusted text must be sanitised to avoid cross-site scripting (Cross-site scripting (XSS)).
Example
This source:
# Title
Some **bold** and *italic* text, and `code`.
- first item
- second item
becomes this HTML:
<h1>Title</h1>
<p>Some <strong>bold</strong> and <em>italic</em> text, and <code>code</code>.</p>
<ul><li>first item</li><li>second item</li></ul>
Preview your own text with the Markdown Previewer, or turn a web page back into Markdown with the HTML to Markdown Converter. The Markdown Syntax Cheat Sheet lists every symbol.