How Come My Walking Script Doesn't Move the Character Forward?

Here’s the script:

function Update () {
   if (Input.GetAxis("Vertical") > 0.2)
       animation.CrossFade ("Walk");

The character animates, but it doesn’t move.

You’re not telling it to move, you’re only telling it to animate.

Depending on how you want to go about moving your character, you’ll likely end up modifying the transform directly (no physics) or applying a force in a direction (physics-based).

Alternatively, you can attach a character controller and it has locomotion built-in.