Markdown is a fairly new markup language (a language that combines text and extra information) that is designed to be easy for a human to read and enter with a simple text editor. If you were using HTML tags and wanted to create formatted text, you would use:
<em>This is some italicized text</em>
<strong>This is bold text</strong>
<strong><em>This is some bold and italicized text</em></strong>
With Markdown, you’d use:
*This is some italicized text*
**This is bold text**
***This is some bold and italicized text***
Markdown plugins are popular for Movable Type and WordPress so it is fun to see this ported to TypePad.
I believe that Markdown was inspired by wiki-style formatting and ease of use for normal non-tech ‘real’ people.