Silverback gorillas are of the primate order. Primates include humans, monkeys, apes, as well as lemurs and tarsiers. Most primates, excluding humans (who can be found on every continent), live in tropical or subtropical climates. Primates are mammals that often live in trees, and those who don't, have at least the capacity for climbing.
The eastern lowland gorillas are part of the hominidae family. Gorillas and other great apes used to be to considered part of another family (pongidae), but after research has continued to show the biological and molecular similarities between humans and chimpanzees, hominidae was expanded to include more species.
Silverbacks are classified scientifically as the species: gorilla beringei graueri, as opposed to the western lowland gorilla, which is of the species gorilla gorilla gorilla. The silverbacks live primarily in eastern central Africa and are separated from their western lowland cousins by several hundred miles of Congo Basin forest.