Significance
The galaxy known as the Milky Way is a large cluster of stars, planets, comets and other celestial bodies that are collected in an enormous, swirling cluster. The bodies nearest the center are huge, dense black holes, super-tightly-packed star clusters and various types of radiation, all of which are partially obscured by thick clouds of dust and other detritus. As the galaxy spirals outward, the "population" density is lessened and at the very edge of one arm of the spiral galaxy is the Earth's solar system.
Geography
In terms of distance, the Milky Way is some 100,000 light years from one end to the other. The Earth is about 28,000 light years from the center of the galaxy, and about 20 light years "above" the plane of the galaxy. To better understand the distances involved, one light year (as a measure of distance) is 9.5 trillion kilometers, or about 5.9 trillion miles. The galaxy itself is relatively flat, like a disk or frisbee. When scientists say that the earth is 20 light years "above" the plane of the galaxy, they mean that it is about 118 trillion miles away from a direct line along the galaxy's disk, but in astronomical terms, that is not very far. Additionally, there are several "arms" of the galaxy, and the Earth is located in the Orion arm.
Misconceptions
Some people still believe, as theologians and scientists did until the 17th century, that the Earth is the center of the galaxy. Seventeeth-century astronomer Galileo Galilei used mathematics to prove that not only does the earth revolve around the sun, but that the earth was not at the center of the universe. For his theories, the Catholic Church persecuted him, forcing him to recant his assertion. Still, Galileo's contributions to the field of astronomy did not go unnoticed, and the conclusions he reached became the basis of modern astronomy and scientific inquiry into the place of the earth in the galaxy.
Size
The immense distance between the Earth and other solar systems preclude realistic travel using existing technology. By comparison, it took the Apollo missions three days to reach the moon, and reaching Mars takes from three to six months. Science fiction is filled with complex mechanisms which allow interstellar travel, from engines that allow faster-than-light travel to wormhole technology where the distance between any two points is brought closer by a tunnel in space. Scientists, however, are unsure that either such system is viable even if they may be theoretically possible.
Expert Insight
Scientists know the composition of the galaxy, and Earth's place in it, through the use of powerful telescopic arrays and devices. The most famous, and productive of which is the Hubble telescope. Because it is based in space, the normal radio signal and atmospheric interference of the Earth is removed, allowing the Hubble to peer deeper into space. The Hubble is so powerful, it technically looks back in time; since it takes thousands of years for light to reach the Earth, by looking at where the light came from, the Hubble actually sees the event closer to when it happened. Thus it peers back in time. The Hubble is also able to see other galaxies deeper in the universe.