Thee, thou, and thine (or thy) are Early Modern English second person singular pronouns. Thou is the subject form (nominative), thee is the object form, and thy/thine is the possessive form.
Before they all merged into the catch-all form you, English second person pronouns distinguished between nominative and objective, as well as between singular and plural (or formal):
thou - singular informal, subject (Thou art here. = You are here.)
thee - singular informal, object (He gave it to thee.)
ye - plural or formal, subject
you - plural or formal, object
Interestingly, when the first English translations of the Bible were being made, the informal thee and thou were used specifically in reference to God to indicate an approachable, familiar God, but as the language changed this paradoxically brought thee and thou to sound more formal to the modern English speaker.