The idea of Lemuria is similar to that of Atlantis. It was originally conceived in the late 1800's to explain similarities between rocks and fossils in Africa, India, and Madagascar. The theory postulated that there once was a land bridge that had joined Africa to the island of Madagascar to the mainland of India. As the theory developed, it tried to account for the existence of lemurs on both Madagascar and India (hence the name.) German biologist Haeckel extended this logic to suggest that man originated on this sunken continent.
More theorists contributed to the theory, extending this sunken continent's reach well into the Pacific ocean. More recently, "Lemuria" has migrated to the Polynesian islands, and even Hawaii.
This theory was also espoused by the occult charlatan Madam Blavatsky in the late 1880's. In The Secret Doctrine, which she claimed was based on ancient Atlantean texts, the ancient Lemurians were egg-laying ape creatures. This was part of the brief Theosophical movement of the time, which generated a wide variety of wild theories and spin-off cults. Some New Age practitioners still refer to Lemuria as well.
There are many books available on this topic.