The meaning of the quote "to thine own self be true" is that an individual needs to always be themselves each day and night no matter what, if they want to succeed in life. The quote explains that a person shouldn’t let anyone try to change him or her to be someone he or she is not.
The quote can be found in William Shakespeare’s "Hamlet Act 1" scene 3, 78-82. It describes how it is important for a person to not deceive him or herself or others by ignoring what his or her heart tells him or her. When a person is true to him or herself, it's easier for that person to be true to everyone else instead of lying to others.