Aspherical lenses are not spherical. Meaning a normal spherical optic is the same curve across the whole lens. The standard for lenses is about 70% of the lens diameter is useful for proper focus. Aspherical lenses change there focal length across the diameter of the lens. This allows the lens to be used to around 85% of the lens diameter. The main aspect of this design allows a lens to have a lower F#. F# is focal length divided by diameter. Lower F# means higher resolution to the camera.
Basically, It allows an optic to be smaller in diameter and still have better light collection than a standard lens of similar size. To a certain degree with modern lens grinding and design techniques, it is a way to cheapen the product while convincing the user it is better and hopefully the manufacturer can convince the buyer it is worth twice the money while saving manufacturing cost. When buying optics, as the diameter of the lens goes up, so does the price. It is cheaper to get more out of the lens than it is to use a larger lens blank at this point.