An object falling straight down under the influence of gravity is an excellent example of constant acceleration in one dimension. Another is an object thrown straight up.
The acceleration comes from the gravitational force exerted on the object by the Earth. The magnitude is determined by the mass of the Earth, the radius of the Earth, and a number called the universal gravitational constant. At the Earth's surface, g, the acceleration due to gravity, equals 9.8 m/s2 and is directed down.