We would like to define what we mean by ”Square-to-Path”.
In the first two pictures we see the club face square in comparison to the path.

In the third picture the club face is open in the back-swing in comparison to the path.

By finding a path where you can maintain the club face of the putter square to your path throughout the whole motion you will be able to repeat this motion time and time again.
Since the club face always is square to your path you will always hit the ball perpendicular to the target line and start the ball onto the line that you are aiming at.