Many people take this to mean "Be true to your own values" or "Don't lie to yourself or delude yourself."
It is stated in Hamlet by Polonious giving advice to his son Laertes. The full text is:
This above all: to thine own self be true,
And it must follow, as the night the day,
Thou canst not then be false to any man.
Farewell, my blessing season this in thee!
What he means here is something more cynical than we take it today.
It means "To your own interests be true. If you take care of yourself first, you'll be able to take care of others."
Ask yourself if Polonious, a man who is spying on Hamlet for Claudius, would be giving high-minded advice.
Mister Wright is correct about "thine". It served the same purpose as German "dein", or Chinese 你的,as opposed to "Ihr" and 您的, respectively.