Inertia and Mass
An object that is in motion, or an object that is at rest, resists changes to that state, and the degree of this resistance is described by the property of inertia. This resistance is directly related to the mass of the object, with more massive objects possessing proportionately more inertia and exhibiting more resistance to changes in their state of motion. For example, think of stopping a small, plastic rolling ball with your hand. It is relatively easy. But you certainly wouldn't attempt to stop a moving car in the same way -- the car is more massive and possesses more inertia.
Aristotle and Motion
For a very long time, it was generally thought that an object that is in motion requires a constant force to keep it that way. This idea originated with Aristotle, and it seems to make sense given your everyday experiences. For example, if you kick a ball, it will eventually stop, and you must keep kicking it to keep it in motion. But this occurrence is only due to frictional forces. New ideas regarding motion and forces were eventually developed and accepted.
First Law of Motion
Experiments that Galileo performed led him to conclude that, in the absence of friction, an object in motion will continue to move with constant speed in a straight line forever. Isaac Newton then refined this idea into his first law of motion, which posits that an object already in motion will continue moving, and an object at rest will remain at rest, unless a force is applied to change the object's state. This law is also called the law of inertia, since it basically defines the concept.
Mass and Weight
Don't confuse the concepts of mass and weight. Mass is a measure of the quantity of matter in an object and is directly proportional to that object's inertia. Weight, on the other hand, depends on the strength of the gravitational field that the object finds itself in. Therefore, a given object will have the same mass and amount of inertia anywhere, whether on Earth, the moon or in distant reaches of the universe. An object's weight, however, can differ, and is not directly related to its inertia.