Acceleration is called the rate of change of velocity of the moving object. If we ignore air resistance then all the objects that are falling on the earth will fall at same rate. Any object that falls freely on the earth has acceleration of 9.8 m/s/s downwards. The acceleration Due to gravity can be simplified as "any object moving towards gravity of the earth".
We can say:

Acceleration produced in a body due to the force of gravity is termed as acceleration due to gravity.

The acceleration due to gravity is defined as the rate of increase of velocity of a body which is falling towards the earth.

The acceleration due to gravity is due to the force by which earth attracts a body of unit mass in the direction of its centre.

Let ‘m’ be the mass of body and F’ be the force of attraction at a distance ‘r’ from the centre of earth then acceleration due to gravity (g) at that place will be

G=F/m=GM_{e}/r^{2}

Where M_{e}=mass of earth

The expression g= GM_{e}/r^{2} is free from ‘m’ (mass of body). This means that the value of ‘g’ is not dependent upon the shape, size and mass of the body. Hence if two bodies of different masses, shapes and size are endorsed to fall freely, they will have the same acceleration. If they are allowed to fall from the same height. They will reach the earth at the same time.

The acceleration of a body on the surface of the earth is g= 9.80 m/s^{2} or 981 cm/s^{2}

Dimensional formula of g is [M^{0}L^{1}T^{2}]
For Example:
1. Drop a book and a paper, you will find that the paper does not accelerate or move downwards as much as the book, because the small force of gravity on the paper is being opposed by the force of air friction on the paper.
2. If we drop a feather and a brick at the same time downwards, then the brick will reach at the ground first, since it is less vulnerable to air opposition.