The word "vector" has a lot of meanings, but in computer science and some branches of mathematics, it basically means "list". Of course, we already have Array objects for creating lists in ActionScript. Indeed, vectors are very similar to arrays, but with one very important difference: the elements must be of a specified type.
Here's an illustration of the difference:
var list:Array = ;
// 1, A String, [object Object], [object MovieClip], [object Shape], [object Sprite]
Note that the elements of the array are of all kinds of different types: a number, a string, a plain vanilla object, and several display objects. But suppose we changed list from an array to a vector with elements of the type DisplayObject:
var list:Vector.<DisplayObject> = new Vector.<DisplayObject>();
list.push(1); // throws TypeError
list.push("A String"); // throws TypeError
list.push(new Object()); // throws TypeError
Now the elements must be of a particular type, and attempting to add objects of any other type will throw an error.
Note the syntax for specifying the type of the vector's elements. This is actually an early introduction of parameterized classes, which are going to be part of the ECMAScript 4.0 standard. (They're already features of languages such as Java.) I was surprised that they'd include an ES4 feature so early, but it seems to be implemented only for vectors. I was unable to make my own parameterized classes in the alpha version of Flash CS4. Also, since Vector is a final class, you can't make subclasses, parameterized or not.
Even so, it'll be great to finally have some kind of type-safe collection. I can't tell you how many times I've had to make my own specialized, type-safe classes for this kind of thing.
Vectors will also improve performance, since the compiler can optimize code for vectors of integers, etc. When initializing a vector, you can also fix its length, allowing for further optimization. For example, to store a 3D spatial position as a list of exactly 3 numbers (x, y, and z coordinates), you can use:
var point3D:Vector.<Number> = new Vector.<Number>(3, true);
Can't wait to start using these....