c# – Playerbody is turning, but not moving in direction turned

So, I have a simple WASD script, and I’ve added a part so when Mouse X is moved, the playerBody (character) rotates in that direction, so, when W is pressed (to go forward) the player does not move in the direction turned, but it moves in the same direction. Although the playerBody has turned, the player still moves in the same direction…. why?

using UnityEngine;
using System.Collections;

// This script moves the character controller forward
// and sideways based on the arrow keys.
// It also jumps when pressing space.
// Make sure to attach a character controller to the same game object.
// It is recommended that you make only one call to Move or SimpleMove per frame.

public class Move : MonoBehaviour
    CharacterController characterController;

    public float speed = 6.0f;
    public float jumpSpeed = 8.0f;
    public float gravity = 20.0f;
    public Transform charBody;
    private Vector3 moveDirection = Vector3.zero;

    void Start()
        characterController = GetComponent<CharacterController>();

    void Update()
        if (characterController.isGrounded)
            // We are grounded, so recalculate
            // move direction directly from axes

            moveDirection = new Vector3(Input.GetAxis("Horizontal"), 0.0f, Input.GetAxis("Vertical"));
            moveDirection *= speed;

            if (Input.GetButton("Jump"))
                moveDirection.y = jumpSpeed;

        // Apply gravity. Gravity is multiplied by deltaTime twice (once here, and once below
        // when the moveDirection is multiplied by deltaTime). This is because gravity should be applied
        // as an acceleration (ms^-2)
        moveDirection.y -= gravity * Time.deltaTime;

        // Move the controller
        characterController.Move(moveDirection * Time.deltaTime);

        float MOUSEY = Input.GetAxis("Mouse Y") * speed * Time.deltaTime;
        float MOUSEX = Input.GetAxis("Mouse X") * speed * Time.deltaTime;

        charBody.Rotate(Vector3.up * MOUSEX);