Markdown is a markup language, which can be used by users to indicate formatting hints to the underlying system. For example, you want a text to be bold, a markup language lets you tell that to the website in a way it understands.

Older markup languages tended to be verbose and complicated. For example, this is a numbered list in BBCode, which is the classic forum markup language: [ol][li]Item one[/li][li]Item two[/li][/ol].

Markdown keeps it simple and intuitive, for the most part.

1. item 1
2. item 2

The above is a numbered list in Markdown. Much simpler than the BBCode version. Simple enough that people like you can do it without even being aware of Markdown at all.

*This is cursive text*
**This is bold text**

# this is a heading

## this is a smaller heading

###### usually up to six levels are supported, but this might differ based on the implementation (my instance seems to make all of these the same size)

> this is a quote
it can span multiple lines too

this is a bullet point list:
- item 1
- item 2

[Links are more complicated, but still as easy as they can be](https://example.org/)

The above doesn't actually display formatted because I used a code block to show the Markdown as written. The below is how the above actually displays:

This is cursive text This is bold text

this is a heading

this is a smaller heading

usually up to six levels are supported, but this might differ based on the implementation (my instance seems to make all of these the same size)

this is a quote it can span multiple lines too

this is a bullet point list:

• item 1
• item 2

Links are more complicated, but still as easy as they can be

edit: this is what the original creator of Markdown has to say on the matter:

Markdown is intended to be as easy-to-read and easy-to-write as is feasible.

Readability, however, is emphasized above all else. A Markdown-formatted document should be publishable as-is, as plain text, without looking like it’s been marked up with tags or formatting instructions. While Markdown’s syntax has been influenced by several existing text-to-HTML filters — including Setext, atx, Textile, reStructuredText, Grutatext, and EtText — the single biggest source of inspiration for Markdown’s syntax is the format of plain text email.

To this end, Markdown’s syntax is comprised entirely of punctuation characters, which punctuation characters have been carefully chosen so as to look like what they mean. E.g., asterisks around a word actually look like emphasis. Markdown lists look like, well, lists. Even blockquotes look like quoted passages of text, assuming you’ve ever used email.