Species diversity is a measurement of species richness and species evenness. Species richness is the number of species.
Species richness is the number of species found in a community or ecosystem.
Species diversity is a measurement of species richness combined with evenness, meaning it takes into account not only how many species are present but also how evenly distributed the numbers of each species are.
For example, if two communities both have five species, species richness would be five for both communities. If the first community had 100 individuals and 80 of them were all one species, this would not be a community with a very even distribution. If the second community had 100 individuals, with 20 individuals belonging to each of the five species, this community would be more evenly distributed. Because it was more evenly distributed, community two would have a greater species diversity.
In the image below, community one would have a greater species diversity because the spread of species is more even.