In short, the definition of Myopia (short sightedness) is where the eye is longer than normal or the cornea is too steep, meaning that light rays focus in front of the retina. Near objects are clear, but distant objects appear blurred. For the most part, this is an inconvenience considering how frustrating it can be to be dependent on contact lenses or spectacles.
In addition, eyes with a high degree of Myopia are at an increased risk of developing a serious condition like retinal detachment or glaucoma.
In short, the definition of Hypermetropia (long sightedness) is where the eye is shorter than normal or the cornea is too flat, meaning that light rays focus behind the retina. Light rays from close objects such as pages of a book cannot be focused on clearly by the retina. Someone with hypermetropic eyes may find their vision is blurred when looking at objects near to them, and for vision to be clearer when looking at far away objects.
Placing a plus powered (convex) lens in front of a hypermetropic eye allows the image to be moved forward allowing for correct focus on the retina. A degree of long-sightedness is common in many people, although this only presents a problem when our ability to see is significantly affected or where headaches and eye strain are common.