An object falling straight down under the influence of gravity is an example of constant acceleration in one dimension. Another example is an object thrown straight up.
The acceleration comes from the gravitational force exerted by the Earth. The magnitude is determined by the Earth's mass and radius, and the universal gravitational constant. At the Earth's surface, g, the acceleration due to gravity, equals 9.8 m/s2 and is directed down. An object speeds up by 22mph for each second it is falling!