it means the elements of the lens are not spherical
imagine a sphere, if you took a slice off it, the curvature on the front surface would be even from point to point
Imagine a traditional flying saucer shape - the curvature in the centre is more than at the edges (where it is flatter). In other words, the curvature (and power) of the lens surface changes from point to point
Spherical lenses are very easy to manufacture, as the tooling that makes the lens is essentially swept on a even curve> Aspherical lenses are harder to manufacture, hence the price difference
Up to now, I have only considered one surface of one element of a lens
Lens designers can choose the power and sphericity of all surfaces of all elements of lenses
The reason aspherical lenses were first used was to counteract distortion (pincusion type distortions). Lens designers can now choose to make a series of elements in a "lens" from a range of materials and curve designs to counteract many other distortions (TCA, LCA etc)
The other spin off with many Aspherical lens designs is that each element tends to be thinner and flatter
Just because a lens is marketed as Aspheric, doesn't mean all the elements will be, generally it is only one or two elements that get the specially designed curve