The markup in question is coincidentally called Markdown, created by John Gruber, author of the Daring Fireball blog. The original source of Markdown can be found at Daring Fireball – Markdown.
There are many Markdown dialects, the documentation for Github’s can be found on the Github Flavored Markdown page.
nice tip from that page:
press M on any Github page with a Markdown editor to reveal the cheatsheet.
You can also use the Github Markdown Live Preview page to test your Markdown documents.
Update 2012-11-08: Efforts are underway to standardize the Markdown syntax. See The Future of Markdown – Jeff Atwood, Coding Horror and W3C Markdown Community Group.
Update 2014-09-09: CommonMark a markdown standard and spec has been released.