Helena Petrovna Blavatsky was a Russian immigrant that arrived in New York City in 1873. She had some experience with occultism and mediumship in Russia and Europe, and became involved with the local Spiritualist scene. Spiritualism was a religious movement focused primarily in the United Kingdom and the United States which focused on communication with the spirits of the dead, often through the agency of a physical medium, table rapping, seances, etc.

In 1875 she claimed to have come into contact with an occult group called the Brotherhood of Luxor. Egypt was a byword at the time for genuine occultism and magic, and claiming association with an existing group was a way to claim authority. She managed to convince an associate Henry Steel Olcott that she was a genuine mystical adept, in contact with this group, and they formed a "Miracle Club" which was eventually renamed the Theosophical Society.

But this wasn't Theosophy as we understand it. Blavatasky was working on that, and in 1875 she started writing her first book Isis Unveiled*, which wasn't actually published until 1877. The book provided the first approach to Theosophy, which was a mash-up of Western occultism, Oriental esotericism, contemporary scientific concepts, and outright fiction - there was quite a lot borrowed from Edward Bulwer-Lytton's novels Zanoni (1842) and Vril: The Power of the Coming Race (1871). Nominally, the book was based on certain unique or obscure occult manuscripts that revealed all these secrets, but a lot of the erudition is kind of faked - she'd copy quotes from books and never cite the book she copied from, that kind of thing. This brought charges of plagiarism from William Emmett Coleman.

The success of Isis Unveiled sort of gave direction to the organization, which revived from yet another New York club to a viable effort. In 1879 Blavatsky and Olcott moved to India, where they became associated with Indian independence movements, and gained some real popularity as these white people in India that were promoting indigenous Indian religions. Blavatsky and Olcott both converted to Buddhism, and were obviously interested in the more esoteric elements of Buddhist religion, especially Tibetan Buddhism, and they Alfred Percy Sinnett, who would condense and popularize her ideas in a book titled Esoteric Buddhism (1883).

All this time, the Theosophical Society was expanding. It was largely following the Masonic lodge model (except that it allowed both male and female members), where an individual would go to another city and have permission to create a new group under the authority of the main Theosophical Society back in India. This sometimes led to individual ideas and internal political disputes. This is important because Blavatsky moved from India to the United Kingdom for her health, and in 1885 one such schism had her create her own lodge in London, the Blavatasky Lodge, which would become very influential, and she formed an "inner order," the "Esoteric Section" of the Theosophical Society, and because she couldn't find anyone to publish her works, she founded the Theosophical Publishing Company, which published her next book, The Secret Doctrine (1888-1889).

Which when you think about Theosophy today and what it is, The Secret Doctrine is what people are talking about. It takes the basic ideas of Isis Unveiled and it really expands on them, especially pushing heavily both the esoteric Buddhist ideas. She claimed now that the "Brotherhood of Luxor" is the "Great White Brotherhood" and writes out this whole cosmology where she claims that the occult manuscript she has, the Stanzas of Dzyan, have revealed at Earth was founded by these alien spirits and that humanity has developed biologically through several "root races" - and still is in development. So it was directly reflecting 19th century science, including race science, and also 19th century understanding of occultism, showing this "secret history"...and people bought it, it became really big and tremendously influential on pulp fiction, occultism, comic books, etc.

So The Secret Doctrine is really the codification of what Theosophy believes, and if you want to get an idea of what Theosophists believe, read that.