You can get some insight into KE from an introductory physics text which derives it from
W = Fd = max...a change in velocity of a mass times a distance traveled.
the KE of a body in motion is equal to the work it can do as it is brought to rest...so it's based on a useful, convenient definition.
For a deeper understanding, check the relationship with potential energy (PE) because in some instances they are equal in magnitude and opposite in sign...as in throwing a ball vertically in the air for example...when the decreasing velocity (decreasing KE) is replaced by an equal increase in magnitude of PE as the ball rises. Things reverse as it falls.
In relativity, things get more complex because each inertial (constant velocity) observer measures the apparent velocity of an object differently...so each thinks (correctly) the object has a different KE.
Parts of the Wikipedia write up on KINETIC ENERGY are easy to understand; some are opaque.
http://en.wikipedia.org/wiki/Kinetic_energy
from a post above: "...which together with the invention potential energy is constant over time... not sure exactly what this means, but in general it is not accurate.; see my example where this is true...with regard to a ball rolling on a flat surface, it is NOT.