Ok, so I need to set the Transform position of a GameObject to the X and Z coordinates of wherever the Mouse is pointing.
I think there was a function for transforming screen coordinates (Mouse position) to World Coordinates, but I'm really unsure on how to do so.
There are lots of things to consider when doing this such as camera perspective distortion, etc, but the simple approach you seem to be describing would the ScreenToWorldPoint which converts a screen point to a world position on a plane parrallel to the clipping planes like this:
transform.position = Camera.main.ScreenToWorldPoint(Input.mousePosition);
but that will have a distance of 0 from the camera. You probably want something more like:
var screenPoint = Vector3(Input.mousePosition);
screenPoint.z = 10.0f; //distance of the plane from the camera
transform.position = Camera.main.ScreenToWorldPoint(screenPoint);
If the object is supposed to be constrained to the XZ plane (or any plane), another option would be to use Camera.ScreenPointToRay() to generate a picking ray, and then intersect it with the plane in question to yield the corresponding world position. (The Unity 'plane' struct has a raycast function that you can use for this.)