A person looking at a person wearing a shirt with a pattern comprising vertical and horizontal lines is able to see the vertical lines more distinctly than the horizontal ones. What is this defect due to? How is such a defect of vision corrected?

The defect is called Astigmatism. When the curvature of the cornea plus eye-lens refracting system is not the same in different planes, this defect arises. As vertical lines are seen distinctly, the curvature in the vertical plane is enough, but the curvature of the lens system is insufficient in the horizontal plane and, the lines cannot be seen distinctly. 

This defect is removed by using a cylindrical lens with its axis along the vertical plane.