It’s treating your variable as a string, the zeroth element of which is [
.
This is happening because your string is not valid JSON, which should use double-quotes as a string delimiter instead of single quotes. You’ll then have to use single-quotes to delimit the entire attribute value.
If you fix your quotation marks your original code works (see http://jsfiddle.net/ktw4v/12/)
<div data-stuff="["a","b","c"]"> </div>
var stuff = $('div').data('stuff');
When jQuery sees valid JSON in a data attribute it will automatically unpack it for you.