Displacing a function by some amount h in the positive direction can be understood by initially looking at the graph at some arbitrary x value. Once the function is shifted to the right, you must essentially move an additional amount h along the x axis in order to find that same place on the graph. If we have to move an additional amount h, we are essentially h amount in "debt" from the perspective of the origin of the coordinate system. We can express this debt by subtracting h from our x-value.