Hypermetropia is the scientific term for long sight. This happens when the light from an object forms an image behind the retina. This could be because the eye is too short, or the cornea or crystalline lens does not bend the light enough. A person with hypermetropic vision has blurred vision when looking at objects close to them, and more clear vision when looking at objects in the distance.
If you place a convex lens in front of a hypermetropic eye, the image is moved forward and focuses correctly on the retina. The result is that a hypermetropic person can then see objects that are both in the distance and close to them clearly.