There are two transformations going on. The first of which is the horizontal or x translation (aka shifting) where the 'x' turns into 'x-1'. This moves the xy axis 1 spot to the left, giving the illusion that the graph moves 1 unit to the right.
The "-3" at the end shifts the graph down 3 units. If g(x) = f(x) - 3, then g(x) is the output of f(x) but 3 less than that, which is why it shifts down 3 units.
