This elements meant to reduce the level of distortions and to improve the sharpness at the image borders.
Basically aspherical elements can optimize the focus of edge and center light rays (see picture below). It is very popular to
name a lens e.g. "28-80 aspherical" in these days but the word "aspherical" does not reveal the effectiveness and quality of
the aspherical element.
There're three types of aspherical elements:
Hybrid asphericals are quite cheap to produce and widely used for cheap consumer grade zoom lenses.
Basically it's a spherical glass lens with an additional plastic surface which forms the aspherical shape. Ground aspherical lenses consist of glass only (obviously). The grinding process of a spherical element and
the following polishing process is very expensive so you only find them in Pro-class lenses like Canon 16-35mm F2.8
and a few older lenses.
Molded aspericals are produced by directly molding glass in a molding machine by incorporating an aspherical metal die.
These elements are often used in good amateur class lenses.
The gain of quality by using hybrid lenses seems to be quite limited while lenses with true ground aspherical lenses often produce
outstanding results, molded aspericals are in between quality-wise.
The best wide-angle lenses use a large diameter aspherical element in the front group
Rear aspherical elements (=smaller and therefore cheaper) are less effective.
Aspherical Elements are used in Nikon, Pentax, Canon, Pentax and other good brands binoculars as well.