WOW... a great question and one I really had to research to answer.... here goes...
Element - each individual piece of glass in the lens
Group - Several elements optically cemented together to act as a single element.
(copied to the running dictionary)
A lens is composed of a number of glass parts, or elements, some standing alone and others optically cemented together forming groups, thus the statistics.
A lens might be made of of 5 elements in 5 groups, meaning that each element stands alone within the lens or it might be made of of 5 elements in 3 groups, meaning that at least one glass construct within the lens design comprises more than 1 chunk of glass. Possible combinations might be 1, 1 & 3 or 1, 2 & 2 -- both combinations allowing for 5 elements in 3 groups.
As to why, optics is a complex subject. Every time you bend light, as with any simple lens, most goes where you want it but some doesn't. Complex lens formulae comprising multiple convex, concave and aspheric elements are worked together using mathematical computer modeling (it used to be done by hand) in order to ensure that all the light gets to the same place -- your sensor -- and at the same time. In the process, the lens designer works out compromises for focal length, aperture, zoom ratio (if any), chromatic and spherical aberrations, pincushion and barrel distortions, coma, a host of other problems.
Groups and elements give you an idea as to the complexity of the optical formula of a lens -- not its quality.
(taken from
http://forums.dpreview.com/forums/read.asp?forum=1030&message=21571821 )