The word thine, when used as an adjective, has an archaic origin meaning thy. It is used in particular before a word which begins either with a vowel or with the letter 'h'. It is a possessive form of the word thou.
When used as a pronoun it again has an archaic meaning. It has come to mean 'that which belongs to thee'. It is used with no following noun, used as a pronoun which is corresponding in meaning to thy, the adjective. The term 'thine' is typically used in language that is ecclesiastical or literary. The term thy is the possessive form of the term thou and is employed as a modifier ahead of a noun.
The word has its roots in the Middle English term thin; coming from the Old English term thIn, meaning thy.