It can indicate two things depending on how you look at it.
g = 9.81m/s2 indicates that if you were on Earth, and you somehow were able to create a space free of any air (a vacuum), and you dropped something, then that object’s speed would be 9.81 m/s after one second, 19.62 after another second, 29.43 after another and so on. In another word, it would accelerate at a rate of 9.81 m/s2.
The purpose why it has to be in a vacuum is because the object would be immersed in air otherwise. And the air would begin it to slow down, for the same reason why something fell in honey takes so long to reach the bottom of the pot: viscosity. The air or the honey would pull on the object as it fell, inducing it to experience an acceleration smaller than 9.81 m/s2. In fact, the pull is equal to the square of the velocity of the falling object, so the faster it gets, the stronger the pull of the air.
At some position, the pull of the air just matches that of gravity, and the object stops accelerating and falls at a constant velocity for the remainder of its descent. That velocity is called terminal velocity. The result is much less pronounced in the air than in honey because air’s viscosity is much smaller: air flows easily.
It has to be on Earth because of the gravitational force changes with distance, and the mass of whatever is stretching, which is Earth. If you were on the moon, g would be changed from what it is on Earth, about a sixth of what it is, because of the change in distance, and the change in mass. The genuine formula for the force of gravity is called Newton’s law of Universal Gravitation, and is:
Wherever M and m are the masses of the two things, G is a universal constant for gravity with a value of 6.67 Nm2/kg2. R is the distance between the two objectives, and the minus sign is just there to get the direction right.
g is derived from this formula. M is fixed, because it represents the mass of the Earth, and R should change, since it is the distance from the center of the Earth to the object under study, but the Earth is large so any small change in R due to the object’s height can be neglected, so R can be taken to be a constant, the radius of the Earth. Since g is the acceleration due to gravity on Earth, you can divide F by m to obtain it, since F = ma.
Thus:
Where the minus sign was neglected because you are more interested in the magnitude of gravity on Earth than its direction. If you wander over far from Earth R will change significantly, so g must change as well, and if you change astronomical bodies, M must change.
Thus g = 9.81 m/s2 indicates that on Earth, in a vacuum, if you were falling, you would accelerate at a rate of 9.81 m/s2, regardless of how your mass.
g can also be taken to indicate the strength of the gravitational field. The gravitational field is how the force of gravity gets shifted across space. Gravity does not require the two interacting bodies to be in contact with each other, otherwise, no life would exist on Earth from touching the sun. There is some distance between Earth and the sun and gravity are transported through them through the gravitational field.
The gravitational field is described as the force of gravity per unit mass of a source. The intensity of the field is just its magnitude. In other terms, the strength is:
Which is correct the similarly as the acceleration due to gravity.
The connection between the strength and the acceleration may not seem to be much, but it is in fact very important. It is for this reason that all falling objects experience the same acceleration.
Gravity is the only force that has this feature. If you compared it to the very similar Coulomb force, which is essentially the same as Newton’s gravitational law, but with charges displacing the masses, you see that for different masses, the Coulomb force effects different accelerations, whereas gravity does not. It is this field of gravity that prompted Einstein to formulate the theory of General Relativity, where gravity is described in terms of geometry.
Gravity is most correctly described by the general theory of relativity (proposed by Albert Einstein in 1915) which represents gravity not as a force, but as a consequence of the curve of spacetime caused by the uneven distribution of mass.
