What is the definition of short-sightedness?

"Nearsightedness" is the word used in the U.S. for what the British call "shortsightedness." The actual medical term is "myopia."

In practical and generic terms, it means that your uncorrected near vision is good but your uncorrected distance vision is blurred and out of focus. Myopia is typically caused by the eye growing (starting in the developmental years) to a "larger than normal" diameter. You may read how nearsightedness is when the "eye is too long." While this is technically true, it suggests that the eye shape is elongated like a sausage -and you will even see cross-section drawings of the eye that show this. But in reality, the larger size diameter of the eye is actually similar in all directions, across and top to bottom, not just along the visual axis from the center of the pupil to the macula (at near the center) of the retina.

The focusing parts of the eye are at the front: the cornea, pupil, and the natural lens (called the "crystalline lens" in anatomy books). They do not "know" that the eye is abnormally long, so they focus an image of a distant object a certain standard distance back towards the retina. But that is not where the retina actually is in a myopic eye-it sits even further back, so the image of a distant object comes to a focus too soon and is blurred when it reaches the retina.

Concave lenses (thicker at the edge/thinner at the center) push the image further back in the eye to account for the extra distance. The default focal point for a "too big" eye is closer to your eye than normal. Middle-aged people who have begun to suffer blurred reading vision when wearing their myopia-correcting glasses often discover that if they remove their distance glasses, they can see much better up close than with them on. This is because they are using the closer default focal point of their nearsighted eye to cancel the negative effects of Presbyopia -the farsightedness from the slow hardening of the natural lens.