Just tip when moving an object https://www.youtube.com/watch?v=WGV5LPLwMgk

In this tutorial to unity, he makes a river and animates it. But at 1:12
 when he moves the object it moves the "waves" in that direction. 

But when I try to do it just does the moves at 1:09
I am completely new to the blender I have been stuck on this for ages....
Thank you for your help or any type of advice!
If i understood is that you need the wave to be moved.

Add a Empty 

In the Displacement Modifier tab -> Texture Coordinator -> Object

Below in object select empty. Select the axis which you want to move in my case its Y axis



Select the empty and move it.

You get this result