William Scott-Elliot was born in 1849 and died in 1919. He was the 10th Laird of Arkleton. Arkleton is located in Scotland. During his lifetime he was an important member of the London Lodge, one of the first centers for the Theosophical Society. His work in the Theosophical Society was highly influenced by one of its three founders, Helena Blavatsky
Theosophy is, as the name suggests, a mix of numerous different theologies and philosophies. Religious scholars classify Theosophy as both a new religious movement and as part of the occultist trend in Western Esotericism. Theosophy takes its inspiration from several western religions, mainly Christianity and Judaism, and from Eastern religions, primarily Hinduism and Buddhism. Theosophy claims that no religion completely summarizes the truth behind the universe, but that by combining many religions and theologies the full truth can be cobbled together.
Theosophy does not reject the results of scientific findings, but stresses the importance of finding the bridge between science and theology. This sometimes involves bending the scientific results to fit the theosophic worldview. Much of the evidence that it draws upon to explain its system of core beliefs comes from pseudoscience and especially psuedoarchaeology. Two pseudoarchaeological elements that are especially important to theosophy are the lost continents of Atlantis and Lemuria. 
The Theosophical Society was created by Helena Blavatsky in 1875 as a branch of Theosophy that deviated from the beliefs of the other founders, Henry Olcott and William Quan Judge. This version of Theosophy (sometimes called Blavatskian Theosophy) focuses on the idea that civilization is cyclical and comes from different root races as described in The Secret Doctrine.  The Secret Doctrine was meant to comprise four volumes, but only two were published by Blavatsky during her lifetime. The first volume attempts to explain the origin of the universe, and relies heavily on Hinduism to compose its core beliefs regarding the cyclical development of the universe. The second volume details the root races, several of which she claims to have originated on the lost continents of Atlantis and Lemuria. She specifically disagrees with Darwin's theory of evolution, saying that mankind is not descended from a common ancestor with apes. Mankind is instead descended from the third root race, which inhabited Lemuria, and the fourth root race, (which descended from a subrace of the third) who inhabited Atlantis. She believed that the people of Atlantis were the ones who created Stonehenge, and also that they reproduced with "she animals" to produce gorillas and other apes. She then returns to conventional Atlantean myths by positing that the island of Atlantis sunk to punish the Atlanteans for their behavior.
Theosophy's Borrowed Framework
Most of the logic and world building for this branch of Theosophy are borrowed from Hinduism and Buddhism. In Buddhism, Maitreya is a future incarnation of a buddha, while Blavatsky fashioned into him into a messianic figure for Theosophy, writing that he would would precede the coming of the fifth root race. Another theme taken from Buddhism is reincarnation. Both Theosophists and Buddhists believe that the purpose of life is to free the soul through the continual gain of knowledge, with the end goal being complete enlightenment. Souls go through the cycle of reincarnation until they reach enlightenment. Blavatsky detailed her entire system for spiritual development/enlightenment in a book that she called The Voice of the Silence.
However, Blavatsky did not originally fold the concept of reincarnation into her version of Theosophy. From the 1870s to the early 1880s she based her teachings off of her book Isis Unveiled in which she said that after the death of one's body, one's soul continues to move on through more spiritual dimensions. After publishing The Secret Doctrine she changed her theology to include reincarnation.
William Scott-Elliot's Contributions
William Scott Elliot was mostly concerned with the lost continents of Atlantis and Lemuria, and the races that inhabited them.