Practicing away form the piano means different things to different people. Karl Leimer, the teacher of Giesking, believed that a piece should be memorized before you play it on piano, so for him, practicing was studying.
For me, it means for the most part planning. Any piece we learn is going to be complex. if you have a 5 person family, you don't go to the grocery store without a list. You can save yourself a lot of time, by deciding away from the piano exactly what you are going to do on the piano. Since practicing consists of discovery, decision, and repetition, you can make discoveries and decisions away from the piano, and enter them into your physical memory at the instrument.
Another idea of practicing away from the piano is visualization. you visualize how the music will sound, feel, and look. When you approach the piano, you approach it from the standpoint of knowing the end goal already, from practicing and visualization away from the keyboard, and then your task is to realize and retain it.
I think it is not important that practicing mentally has to be linear. What I mean is, you don't have to sit there and try and think of the whole piece from the first note to the last. You have to address what needs to be practiced at the keyboard, and the whole form will come together for you later.
Walter Ramsey