In Greek mythology Ariadne is the daughter of Pasiphaë and King Minos of Crete. She fell in love with Theseus and gave him the thread with which he found his way out of the Minotaur's labyrinth after killing the Minotaur.
The expression "Ariadne thread" is the solving of a problem with multiple apparent means of proceeding - such as a physical maze, a logic puzzle, or an ethical dilemma to trace connections between different parts of what seems like an impenetrable maze.
I like to think about Ariadne's thread as the certainty that in the most difficult circunstances there is a thread to show the way out. Just pick a color and go.