What is Theosophy?

The word comes from the Greek theos, meaning god or divinity, and sophos, meaning wise. Such wisdom being derived from insight and experience as well as intellectual study.
(The Greeks used the word 'god' to signify a divine being - not in the way we use the word in it's modern context)

One origin of Theosophy is with the Ancient Egyptians - in particular a priest called Pot-Amun, who lived in the early days of the Ptolemaic dynasty. It is also said that the name signifies one consecrated to Amun, the God of Wisdom.

Theosophy is a religious philosophy also known as the Wisdom Religion. Those that follow this path believe in one absolute, incomprehensible and supreme Deity, or infinite essence, which is the root of all nature, and of all that is, visible and invisible. They also believe that man has an eternal immortal nature, because, being a radiation of the Universal Soul, he is of an identical essence with it.

While the modern theosophical movement can be traced back to Helena Petrovna Blavatsky and her teachers, it is part of a spiritual movement that is perhaps almost as old as thinking humanity. Its philosophy may be seen as a contemporary presentation of a perennial wisdom underlying the world's religions, sciences, and philosophies. Theosophical concepts are not dogmas; only the ideas that have value need be accepted. Theosophical books are considered neither as revelation nor final authority, but as guides in the individual's search.  

To quote H. P. Blavatsky herself attempting to answer the question What is Theosophy?

Theosophy is, then, the archaic Wisdom-Religion, the esoteric doctrine once known in every ancient country having claims to civilization. This "Wisdom" all the old writings show us as an emanation of the divine Principle; and the clear comprehension of it is typified in such names as the Indian Buddh, the Babylonian Nebo, the Thoth of Memphis, the Hermes of Greece, in the appellations, also, of some goddesses -- Metis, Neitha, Athena, the Gnostic Sophia, and finally --the Vedas, from the word "to know." Under this designation, all the ancient philosophers of the East and West, the Hierophants of old Egypt, the Rishis of Aryavart, the Theodidaktoi of Greece, included all knowledge of things occult and essentially divine.