Geometry is a big part of optics. Don't think of it as something other than the picture, it's what makes the picture.
An aspherical lens does not suffer (so much) from spherical aberration. That's
a fancy term for "the rays of light do not meet exactly in one
distance from the lens". But what's exactly in one distance from the
lens? Right, the sensor or film of the camera. If you have spherical
aberration in your image, some parts of it will be blurry (out of
focus) even if they should be sharp because the rays do not meet
each other exactly on the sensor (they meet a bit in front or behind
it). The further from the sensor the rays come into the lens, the
more pronounced will this problem be.
That's why the cool kids are always bragging about the corner
sharpness of their lenses. That's where it pays off to have
Well, "advertised as" plays an important role here. It sounds
technical and can attract buyers. Lenses are often lens systems that
are made out of several elements. Usually not all elements are
aspherical, because the production of such elements is more
expensive than the spherical ones. Optical systems have a lot of
properties you don't even hear about or only hear about
insufficiently making them useless for comparison.
For example: a lot of lenses have a stabiliser, to prevent camera
shake. But how does one compare to the other? The information is
limited to them having a stabiliser. What exactly does it mean to
have weather sealing? Can it be dropped in the mud, used in a hail
storm or what?
But sure enough, not mentioning them will make your product look
worse than those of other vendors.
Don't worry so much about these marketing buzz words.
If you are not sure what lens to buy, read about them. This will give you an estimate of their strengths and weaknesses. If you still can't decide, rent both. Preferably at the same time and compare them for yourself.
And remember that it's you who takes the picture, not the asphericitillityness* of your lens.
*that totally is a word