What's an analog tool? Simple, something that doesn't require circuitry or higher technology to function. A cell phone? Not analog. A rotary phone? technically analog due the moving parts that are essential to its function and, lack of circuits.
But the term 'analog tool' refers to age old technologies to assist work-- such as pens, pencils, chalk, paper, parchment, books. Simple items that require the user to manipulate to achieve work-- no processing allowed!
It is cool to see the resurgence of analog tools in the office and home. I suppose it is due to a few factors that are simply irreplaceable by technology:
1) Slowing down - using an analog tool such as pen and paper causes your mind to ease as it dictates to your body what to write. Writing is proven to improve brain activity and memorization (likely due to the slower nature of the process). Improved memorization is awesome for a few reasons, but most notably, it teaches your mind to retain more information, so the better your memory gets, the better your memory gets and so on.
2) Meditative - a characteristic that is forever linked with 'slowing down'. Taking extra time to do a task can help you relieve yourself from distraction. The act of focusing on a singular task is good for you mind and body and a virtue in many spiritual and religious circles. This type of focus is proven to have powerful stress relieving potential and is a great way to begin or end a day.
3) Less distraction - using a 'screen' device is packed full of distraction potential. Notifications, pop-ups, windows, icons... they are all there constantly whispering at you. When you put those aside for the tactile experience-- it is just you and your thoughts.