About Short-sightedness

Myopia is the technical term for short-sightedness. In practical terms, it means that the eye can clearly see things up close (i.e. at a 'short' distance), but things far away are fuzzy and cannot be seen properly.
The cause of this is that the light entering the eye is focused too quickly. The point of focus therefore lies in front of the Retina, so by the time that the light travels that bit further to hit the Retina, it has begun to de-focus again and the image is fuzzy.

The reason for light focusing too quickly is either that the eyeball is longer than it should be, or that the Cornea or Crystalline Lens is too powerful, or the Refractive Index (i.e. density) of the eye (in particular the Crystalline Lens) is higher than normal.
Myopia is compensated for by a Diverging lens, often known as a Minus Lens. If you are Myopic, your prescription from your Optometrist will have a number with a minus sign (-) in the first box which is usually marked 'Sphere'.

About Long-sightedness

Hyperopia is the technical term for Long-sightedness. It means that far away objects ('long' distance) are relatively clearer than close-up objects. It does not mean that far away objects are definitely clear, nor does it mean that close-up objects are definitely fuzzy. That depends on the amount of Hyperopia, and the age of the person.
Hyperopia is a result of the focusing of light not happening quickly enough, so that the light hits the Retina before it has properly focused. This will lead to fuzziness, except that the eye can often increase its focusing power by a process of Accommodation.

In a perfect sighted young eye, the eye is relaxed for distance vision, and it accommodates for close vision. In the young Hyperopic eye the eye is having to accommodate for distance vision, and has to accommodate even harder for close vision. After the age of 35/ 40 (ish) the ability of the eye to accommodate decreases rapidly, and by 60 years of age there is no real accommodation left.

Therefore the need for spectacles to correct Hyperopia increases with age, and is noticed for reading before distance vision.
Hyperopia is compensated for with a Converging lens, often known as a Plus lens. If you are Hyperopic, your prescription from your Optometrist will have a number with a plus sign (+) in the first box which is normally labeled 'Sphere'.

About Astigmatism

If an eye does not have Astigmatism, the eyeball can be considered to be spherical, like a football (soccer-ball if you prefer the American terminology!).

If you imagine getting a football and placing one hand under it, with the other hand on top of it, and then squashing the ball, it will become distorted. This is what Astigmatism is like: - a natural distortion of the eyeball that causes the light focusing inside the eye to become distorted and out of focus. Astigmatism has an axis, which corresponds to the orientation of the distortion. Imagine squashing the football, but with your hands side by side, instead of on top and underneath - the orientation of the distortion is different, even if the amount of distortion is the same.

Astigmatism is compensated for by a corrective lens that also distorts light, by the same amount as the eye itself does, but in exactly the opposite orientation. The distortion of the corrective lens and the distortion of the astigmatism of the eye effectively neutralise each other to leave a 'clean' focus point.

If you have Astigmatism, your prescription from your Optometrist will have a number in the 'Cylinder' box that follows the 'Sphere' box. The number might have either a minus (-) or a plus (+) sign. The next box on the prescription form will also be filled in with a number to signify the Axis.

Astigmatism can occur on it own, or along with Myopia or Hyperopia.

About Presbyopia

Presbyopia means 'Old Eye', and refers to the reduction in the eyes ability to accommodate that typically occurs around 40 years of age (40 was once considered old, but these days it just feels like the end of an initial very youthful stage!).
The cause is the Crystalline lens of the eye, which normally supplies the variable focus required for different distances. This lens hardens up throughout life - since it starts off extremely flexible, it is only by 40 (ish) that the loss of flexibility actually affects vision.

This means that whatever kind of eyesight you have for distance vision (perfect/ myopic/ hyperopic/ astigmatic), the prescription that you need for reading/ close work will be different.

If you don't need distance glasses, you will need reading-only glasses. If you do need glasses for distance vision, you will either need separate reading glasses, or use Bifocals or Varifocals which both give distance and reading corrections in one pair of spectacles.

If you are Presbyopic, your prescription from your optometrist will have a number in the 'Add' box.