This would be an ArrayCollection which is a wrapper for an Array basically to give you sort and filter function capabilities (and other methods). The constructor optionally takes an Array as an argument, [] is a new array with no elements. [[]] is an array with one element in it that is an array with no elements in it. So this is saying make a new ArrayCollection with it's source as an array which in turn contains one element that is an empty array. Not sure why they would be doing this, but that's what it does.
To sum up, you can declare and instantiate an array in AS3 like:
var myArray:Array = [];
or
var myArray:Array = new Array();
To add since this is I believe ECMAScript specific as well you can instantiate an object similarly using {}. Such as:
var myObj:Object = {};
or
var myObj:Object = new Object();
Either of these sites is good reference material for AS3:
http://help.adobe.com/en_US/as3/dev/WS5b3ccc516d4fbf351e63e3d118a9b90204-7ee5.html#WS5b3ccc516d4fbf351e63e3d118a9b90204-7ee1
http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/Array.html
When I first got started with Flex (having a background in HTML/JS, C, C++, and Java) I found these videos to be really useful (if not always 100% correct/up to date, they explain the overarching concepts):
http://www.adobe.com/devnet/flex/videotraining.html