Question

What is meant by the statement that acceleration due to gravity is 9.8m/s²?

Answer 1

This means that the earth pulls anything towards it center, which gives the pulled object an acceleration of 9.8 meter, each second, during its 'fall' to earth. So the velocity (speed with a direction) of such a body pulled towards the earth increases by about 9.8 meters/second in each second.

This is obtained from;
F=GMm/d² ;
the famous equation of gravity, proposed by Isaac Newton.
And,
F=ma (also proposed by Newton)
So,
ma = GMm/d²
a = GM/d²
= 'g'
≈ 9.8
The value of g(9.8...) is dependent on quite a few factors such as altitude of the place the object being pulled is at, the density differences in various places within the earth, latitude of the location, forces such as centrifugal and centripetal etc. (because the mass of earth, the distance between earth and the object, and external forces - on which acceleration due to gravity is dependent on - vary)

It simply means that a freely falling object would increase its velocity by 9.8 m/s per second.
This can be written as-
9.8m/s/s which is nothing but 9.8m/s^2.