Species richness tells us how many species are present. Their relative abundance adds another part of the picture. Two sites can contain the same number of species while one is dominated by a single species and the other has a more even mixture.
Biodiversity is also discussed at other levels, including genetic variation and the variety of ecosystems. The right measure depends on the question. A species count can be useful, but it cannot by itself describe the condition, ecological roles or long-term prospects of every population.