The appeal is twofold: a lot of engines now understand it and it is (relatively) easy to write by hand. (Except for the bloody links, writing the HTML for them is much easier than the equivalent markdown, I do it infrequently enough that I always mix up the brackets or the order (or both...).)
The way to remember it is just that you're parenthesizing the URL. Naturally, you might write it "look at this thing (http://example.com)" - in Markdown, you do the same, but with brackets to indicate where you want the link to show up. "look at [this thing](http://example.com)"
I don't buy for a second that <a href="http://example.com">this thing</a> is more intuitive than that, even if you disagree about the specific brackets used.
I understand the herd effect - so I put it in user-facing projects that I'm working on - but I don't understand what's driving the herd. Specifically, I don't see any advantages over asciidoc and find it awful to work with.
edit: I do understand this project, though. It'll get rid of the horribleness in implementing markdown, at least.
Reddit uses Markdown. GitHub uses Markdown. HN (sorta) uses Markdown. Wordpress, Tumblr, and Discourse all use Markdown. If I used Markdown for my own User-Generated-Content Textareas™, people might already know it.
If I use Asciidoc, I may as well be using SGML. It's just another (nice!) syntax you're forcing people to cram into their brains.
I'd never heard of asciidoc before this thread. I suspect asciidoc suffered from being associated with docbook? And perhaps it's just that Perl was much more popular for writing forums in than Python, at the time.
Actually, as a C++11 user, it's a lot like a lambda declaration: [capture](parameters){…}. Certainly the brackets are in the same order. The similarity between lambdas and Markdown URL's is actually a nice feedback loop when I'm doing C++11 code.