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What is acceleration?

Physics

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In physics, acceleration is the rate at which the velocity of a body changes with time. In general, velocity and acceleration are vector quantities, with magnitude and direction, though in many cases only magnitude is considered (sometimes with negative values for deceleration, treating it as a one dimensional vector).
source: Wikipedia

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Acceleration is basically the recorded change in the velocity of an object. It is the rate at which the object changes its speed or velocity. Stepping on the gas pedal when driving a car makes it to accelerate.

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The first derivative of velocity. Gravity is an accelerating force.

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did not understood properly
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This is not easy to understand. First you should understand what Newton cane up with for large bodies, then Plank, Heisenberg, Maxwell, Bohr, and others - of course including Einstein, who proved that if you were in an accelerating elevator - upward toward from your feet to the ceiling if the elevator - you would not be able to distinguish this sensation of "gravity" from the kind of gravity we usually talk about - what holds you to the grown. This means that gravity is actually an accelerating force, and is relative, directly related to the mass content of what you are accelerating toward. Scientists have discovered that of the several forces we can identify - weak, strong, electromagnetic, etc., very tiny "force carriers" are responsible for their effects. We've seen this experimentally. What we haven't seen is the force carrier for gravity and it's exact nature of how it is so powerful it can actually "bend the fabric of empty space (aka, "spacetime")" but how? We may have found the force carrier last year at the Large Hadron Collider in Geneva - with the discovery of the "Higgs Boson" (named after Dr. Peter Higgs who came up with the idea back in the 1960's). This discovery would complete "The Standard Model" of physics, of which all reality is based on, in our quest to discover the TOE: The Theory of Everything. Even given that accomplishment - we are still at the beginning of how it all works.
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