Answer: The graph of f(x) has been shifted down 1 unit to get the graph of g(x)
Recall that y = f(x). So saying g(x) = f(x) - 1 is really saying g(x) = y-1. Whatever the y value is, we subtract 1 from it. This visually will shift the point down 1 unit. Apply this to every point on the f(x) curve, and the entire curve shifts down 1 unit.
note: the x coordinate stays the same which is why we don't have any side to side movement.
As an example, I have attached the graph of f(x) = x^2 and g(x) = x^2-1