Answer:
"Acceleration due to gravity" typically refers to the increase in speed of a falling object due to the gravitational pull of the Earth. If jump out of a plane, your speed increases towards the Earth (or the center of the Earth really) due to the acceleration of gravity. If you throw a ball up in the air, it slows down and falls due to the acceleration of gravity.
I guess it's specified because the force of gravity is causing the acceleration in these instances; as opposed to some other outside force.