What would cause extreme blurry vision (cannot distinguish even very large letters) out of only one eye in a child?

Check my list: If this is a new event (the child saw well from this eye a brief period prior to this) then you need to see an ophthalmologist right away. If this has been present for a long time, then it might be some congenital problem with the eye, a very high refraction in that eye alone, a retinal problem from birth, a variety of problems in the back of the eye. This needs to be sorted out with an exam