Here are a few reasons why!
Milder temperatures during initial root growth give roots a great head start.
Fall has frequent rain fall, which allows for more consisted watering during initial root growth.
Even when the temperatures drop to freezing and below the ground temperatures will usually stay above 40, which allows for continued root growth into the winter months. Even if the plant is dormant above ground the roots can continue to establish when the ground temperatures are above 40 degrees.
Flowering shrubs are already established for the following spring which generates better flushing and flowering in the spring as opposed to planting a flowering shrub in the spring. When a flowering shrub is planted in the spring it has to go through its reproductive cycle (production of it flowers) and establish new root growth simultaneously. This creates more stress on the plant than if it is planted in the fall and can already have a start on its new root structure.
Non-flowering shrubs also benefit in the same way as they will have better flushing in the spring if they are planted in the fall because their initial root growth has already been established.