group can be a single element or more than one. A 5 elements lens can have 5 groups, meaning each element stands as one group. Some lenses have more than 3 elements stack together to form a group...as it is difficult to manufacture those element in one piece (thus the combination of several elements to form a group).
It used to be the more you have, the more likely it is that there will be optical distortions, colour fringing, chromatic aberration, etc in your picture. That's why the early zooms, with their complex optical structure, are always lousier than the much simpler prime lenses, which is also why prime lenses are usually very sharp and crisp.
However nowadays, with the introduction of wildly exotic elements, this may no longer be true. Some zooms are equal, or better to primes, but of course, you pay the price accordingly.
With modern optics? No it doesn't matter. Judge the lens based on the quality of the images it produces, build quality and price.
Although the technical details do affect the final product, that's for engineers and designers to worry about. As a photographer, be concerned only about the final product and how it performs. What goes in is really of no direct concern, as long as it delivers where it counts.