The roll program occurred during a shuttle launch for the following reasons:
(...) Orienting the shuttle more parallel toward the ground with the nose to the east.
But why east?
The phrase 'with the nose to the east' is a shorthand. The direction depended on the orbital inclination chosen for the mission.
You usually want to launch to the East (as opposed to launching to the West) because of the Earth's rotation to the East. If you launch to the East, you get part of your orbital speed (about 300 m/s on the equator) 'for free'.
The Shuttle needed to perform a roll program to get to the launch inclination: the launch pad is at a fixed angle that usually doesn't match the launch inclination, so you need to change course (preferably just after launch when your speed is low and the energy cost of the maneuver is lowest).