Thou - thee - thy
(See also Archaic personal pronoun.)
These are archaic forms of personal pronouns. Until the age of Shakespeare, they were perfectly normal; but since then, they have become obsolete in English, except in some very restricted circles - mostly religious.
They were the singular forms of the second person. If a speaker was addressing a single person, that other person was thou, if the grammatical Subject of a Clause, and thee if its Object. If the person addressed was the owner of something, it was said to be "thy possession". So it behaves just like the other personal pronouns - 'I', 'me' and 'my', for example. It's just that nobody nowadays uses it, outside traditional prayers in old-fashioned churches.
When thou was current, 'you' was only used for the plural of the second person. If a speaker was talking to several listeners, they were 'you' - although in the earlier times, this was only the form used for the Object of a Verb. The Subject was 'ye', and the possessive was 'your'.
To begin with, the usage in English was similar to that in many other languages, both European and non-European, today. For members of one's family and for good friends, there is a singular form. In French, for example, this is 'tu'/'toi'. Everyone else, whether singular or not, is addressed by the more respectful and formal 'vous'. (Indeed, there are two verbs in French, tutoyer and vousvoyer, meaning "to call by the form 'tu'" and "to call by the form 'vous'" respectively.) Such a distinction might be useful in English. Alas, it is no longer possible in modern English.