I'm trying to get an object to move using javascript however it won't move, can someone help?

Firstly, try to make sure your code is tabbed correctly, as its very hard to see whats in what condition:

  function Update () {
      if(Input.GetButton("Horizontal"))
      {
          isMoving = true;
      }
      while(isMoving)
      {
          if(Input.GetButton("Horizontal"))
          {
              transform.position.x = movSpeed;
          }
          if(Input.GetButtonUp("Horizontal"))
          {
              isMoving = false;
          }
      }
  }

The while loop is unnecessary, update is called repeatedly once a frame already. Since we want to only change the position when Input.GetButton("Horizontal") is true, we can remove most of the rest of the code too.

  function Update () {
      if(Input.GetButton("Horizontal"))
      {
          transform.position.x = movSpeed;
      }
  }

Now here, we are setting the x position of the transform to movSpeed, so each frame the position of the object won't actually change. We want to add movSpeed to the x position, using += instead of =.

  function Update () {
      if(Input.GetButton("Horizontal"))
      {
          transform.position.x += movSpeed;
      }
  }