A geodesic, or the shortest or longest path between two nearby points, was first suggested by Einstein in his Theory of General Relativity. Einstein proposed that gravity was not a separate force by itself, but the result of the warping of space-time by the mass and energy of a body. This complicated explanation can be seen in this simple example: Put a heavy ball in the center of a trampoline. Notice the curvatures that are created by the ball. Now, a planet orbits the sun because it follows the curvatures that are created by the star. So now send a smaller ball into the curvatures of the trampoline. Notice how the ball begins to rotate around the larger ball. On Earth the smaller ball will eventually stop because of frictions and because it is attracted toward the center by the Earth's Gravity. Yet, in space, these conditions are not present, so the planets in our solar system will always orbit the sun, following its curvatures.
Yet this theory of gravity was not always present. Before Einstein's theory of General Relativity, scientists and physicists were following Newton's theories and Newton's form of gravity. What his theory basically stated was that each object exerts some sort of a pull. This object can be as large as the earth or the sun or anything else, or as small as an apple and even smaller. This ability of any object to exert a pull is shown in this example:
When an apple falls off of a tree, it is influenced by the pull of the earth, which is very strong. But the apple itself exerts a pull that attracts the Earth to it. The reason Newton said the Earth did not jump up to the apple was because the apple exerted such a small pull on the earth that it was hardly measurable.

:: Laugh ::

Einstein's theory basically states that objects just follow a natural course, but orbit, for example like planets, because they naturally follow the curvatures their respective star creates. This theory has been proven by the comparison of the positions of stars at night, and during a solar eclipse. If the curving of space-time really existed, then the position of the star measured during the solar eclipse should be different than the position at night because the light would follow the natural curves and bend towards a certain direction. This assumption proved to be true and the geodesic theory of gravity began to be seriously accepted by most physicists.
There are two aspects that should be pointed out in the Theory of Relativity. The first is that there are, in actuality, two theories, the general theory and the special theory of relativity. The second aspect is the explanation of both of them. Another main idea in the General Theory of Relativity, other than gravity, is that as a person accelerates and begins to approach the speed of light, a significant slowing down of the aging process will occur. This means that say an astronaut leaves the earth in a rocket ship traveling at close to the speed of light, he will age more slowly than the people on Earth will. So for example in ten years for the humans on Earth, the astronaut may return only one year older. The Special Theory explains that this aspect may change depending on the observer. In other words, while the astronaut is leaving Earth at close to the speed of light, the Earth and its people are heading away from him at close to the speed of light as well. So in his view, the humans may get older more slowly than he does because he is the observer. For the humans on Earth, this is vice versa. However, for now there is no way to accurately verify this theory and it still provides as many perplexing questions as it has solved.