Spherical lenses (simple lenses) have a surface which is an 'arc' of a true sphere. The downside is that the focussed light rays from different parts of the surface will fall on a slightly different image plane.
Aspherical lenses (or aspherical elements in a lens) correct this by ensuring (or trying to!) that rays entering at any point on the surface will be focussed on a common image plane.
Wider aperture lenses have increased need to employ aspherical elements as the depth of focus decreases as the size of the aperture increases....for the same focal length.