Myopia, Hyperopia and Astigmatism are commonly referred to refractive errors.
Myopia is often referred to as "short-sightedness" or "near-sighted". An eye is myopic when the "far point"; a point at which light from an object is focussed on the retina, is located at a finite distance in front of the eye. Myopia can be due to either an eye which is too long relative to the optical power of the eye (axial myopia), or because the optical power of the eye is too high relative to the length of the standard eye (refractive myopia). The focus is correctly adjusted with a "minus" power lens, or concave lens.
Hyperopia is often referred to as "long-sightedness" or "far-sighted". An eye is hyperopic when the far point is at a virtual point behind the eye. Generally the hyperopic eye is too short with respect to the refractive state of the standard eye (ie an emmetropic eye or eye requiring no optical correction) or because the optical power of the eye is too low relative to the length of the standard eye. The focus is correctly adjusted using a "plus" lens power or convex lens.
Emmetropia is just another name for an eye that has no optical defects and a precise image is formed on the retina.
An astigmatic eye generally has two different meridians, at 90degrees to each other, which cause images to focus in different planes for each meridian. The meridians can each be either myopic, hyperopic or emmetropic. The correction for astigmatism is a lens power at a particular direction of orientation [ see section 4.1 ] Astigmatism causes images to be out of focus no matter what the distance. It is possible for an astigmatic eye to minimise the blur by accommodating, or focusing to bring the "circle of least confusion" onto the retina.