In any lens, elements are the specific lens pieces used and how are they arranged to obtain a particular feature, the arrangement is the group. Lenses pieces are usually arranged in groups. In lens, say if it is a zoom lens, it will have more number of elements and groups, where as for a prime lens, it will have less number of groups and elements. 

Usually it is termed as the more number of groups and elements, the better the quality but it is not always true. Lens quality also depends on the type of glass, design mechanism, manufacturing process of the lens. So for a particular focal length, a prime lens would be better than the zoom lens.

Prime lenses usually perform better than zoom lenses.