People tend to like it because it's plain text, easy enough to sanitize input, represents most of the typical syntax people already used for a generation in marking up plain text. Doesn't require knowledge of HTML tags, and doesn't introduce the copy-paste pain that WYSIWYG editors introduce.
The thing I dislike about the hubub around Markdown is the incredible poverty of ambition. No-one has yet quite nailed the perfect web-based editor for the kind of styled text we've had in printed matter for 500 years; apparently, because of this, we're all supposed to be excited about an ugly hack for representing styled text which is arbitrarily limited by the computer systems of the 1970s. Sorry, I want something better than that.