A cylinder has zero vertices. A cylinder does not have a vertex because there is no point where two lines meet. This is because a cylinder, unlike a prism, has circular faces; there is no corner where two straight lines meet.
A vertex is where two lines intersect. It is otherwise known as a corner. A triangle, for example, has three vertices while a square has four. Three-dimensional objects tend to have more vertices than do two-dimensional figures because they have more corners than their two-dimensional counterparts. A cube, for example, has eight vertices, and a triangular prism has six.