for example:
let myArray:[] = []
or
let myArray = []
The first one is not possible (it will complain about expected element type) If you don't know the element type you can use AnyObject but if you know the type of it you have to put it there (Int,Double,String, AnyObject, etc...).
var myArrayOfDoubles:[Double] = []
The second one (when omitting the type) is OK ONLY if you initialize it with some values but If you try it with an empty array you won't be able to append anything (at least using Playground) saying that NSArray does not have a member named append.
var myArrayOfInts = [1,2,3,4,5] // [Int]
var myArrayOfAnyObject:[AnyObject] = [] // [AnyObject]
And finally last but not least you have to define it as var because if you define it using let it will stay empty forever :)