I have found two meanings for this rule, one practical and one life changing.
First the practical. Left to our own devises we will start our work at the beginning and work our way to the end. Cognitive science explains some of the phenomenon we experience with this approach. The two primary challenges we encounter involve issues of interference and recency. Interference occurs when new or old material will block or interfere with recall. Sometimes the new material is similar enough to the old material as to create a conflicted memory. (This happens a lot in music!) Recency is the principle that we remember the most recent event better than older events. If we start at the beginning and play to the end we will remember the beginning well because it is the beginning and had our clearest focus; and the end almost as well because it is recent. But the middle is some kind of vague muddle of notes we know we played but have no idea what we did.
If you begin at the end and work backwards toward the beginning; first leaning the last measure and then the next to last measure, playing both; and then adding another measure and so on; each measure has a chance to be the beginning. Your retention of the middle is greatly enhanced.
A few years ago, while reviewing my repertory list I realized that I had learned about 1/3 of Beethoven’s piano sonatas. Into my silly head popped this notion that it would be a good thing to learn and play them all as preludes and postludes at my church. It took several years to complete this project of playing the entire set of sonatas sequentially. When I finally completed the project and had a chance to look back on my work and began to do it again, I had a profound sense of what the poet T. S. Elliot meant by:
“We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.”