Question

What is acceleration due to gravity

Answer 1

The acceleration developed between two bodies containing mass as a result of the gravitational force between them.

Answer 2

If you stay on the same planet and drop a lot of objects one at a time,
it turns out that every object you drop falls from your hand to the ground
with the same acceleration, and hits the ground with the same speed,
no matter whether the object is light, heavy, or anything in between.

That particular value of acceleration is the "acceleration due to gravity".
On Earth, it's 9.81 meters per second².  On the moon, it's 1.62 meters
per second².  On Jupiter, it's 25.89 meters per second².

Why we don't generally notice it:  The previous description is true if the
ONLY force on the object is the force of gravity.  If it has to fall through
air on the way down, then the air can have a great effect on it.  Many
museums have an exhibit where they drop things in a long tube with
all the air removed from it, and there you can see some pretty weird
stuff ... like a bowling ball, a rock, a sheet of paper, and a feather, all
falling together, with nothing fluttering.

Why everything falls with the same acceleration ?  That's a separate question.