What does Nothing is true. Everything is permitted. mean? (Answer in full)

"To say, 'nothing is true', is to realize that the foundations of society are fragile, and that we must be the shepherds of our own civilization. To say, 'everything is permitted', is to understand that we are the architects of our actions, and that we must live with their consequences, whether glorious or tragic."

Basically its this idea of freedom to think and do how we chose while still holding the responsibility of our actions.

If you heard Ezio explain it in deep terms in Revelations, it would be somewhat enough if you can understand.

Simply:
The application of the three tenets in the daily life of the Assassin.

Striving to keep the peace in all things while killing Templars and corrupt officials to preserve freedom.