Aspheric Eyeglasses correct the same vision problems normal lens styles would, but accomplish it using a different lens curvature. Where most lenses feature a similar curvature throughout, aspheric lens types have different levels of curvature based off proximity from the center of the lens.
Aspheric lenses are known to reduce distortion by focusing incoming light entirely on the retina, whereas traditional spherical lenses allow more light to scatter throughout the eye. By virtue of design, Aspheric lenses are thinner and lighter than their spherical counterparts, which is the large reason as to why they’re so popular these days. While there are very few drawbacks to Aspheric lens types, they do typically cost more than traditional lens types due to increased difficulty in manufacturing accurate lenses.
By definition, progressive lenses are a variant of aspheric lenses, but are made specifically for the purpose of correcting both close, and long range vision problems.