I thought more groups and/or elements made it better?
You could have a lens with just one element - but it wouldn't be very good. Each element in a lens "bends" the light but also introduces some errors (couloured fringes, distortion). The lens designer uses several elements with opposite errors so that finally the errors cancel one another out and you get a near-perfect image. The elements may be cemented together in one group or in several groups with a space between each group. On most prime lenses 4-6 elements is enough to get an excellent result.
In a zoom lens there is at least one group of elements that moves in order to change the focal length. On a VR/IS lens there is yet another group that moves to do the image stabilisation trick. The result is a lens with up to 20 elements.
Unfortunately each time light enters or leaves a lens element there is some dispersion resulting in loss of contrast, so there is a limit on how many elements you can have in a lens and still get a usable image. Thanks to progress in lens coatings and glass technology, you can now get very complex zoom lenses that give results that are almost as good as simple prime lenses (the zoom lens still has more distortion).
Example: my 18-200VR gives me better results than my 5 element 28mm f2.8 prime
Charles
Nikon D800, D7200, Sony RX100m3
Not buying any more gear this year. I hope