My sister is big into books. She has thousands of them. One day I was helping her move dozens of boxes of them, carrying them up and down stairs and I realized: All the data in these dozens of boxes would fit on the phone in my pocket. Why was I wasting so much effort to move so little data?
Digital media takes up no more space than a hard drive. It doesn't need dozens of boxes to move, or shelves to store. It won't add clutter to your house.
If your digital media is lost in fire, flood or theft, it can usually be redownloaded at no extra charge. That's insurance worth potentially thousands of dollars.
Digital media opens up new possibilities, such as a searchable index of your content, metadata to easily organize it, notes that don't devalue the original content, and new features such as animated interactive books.
Digital media is easier and more convenient to shop and purchase. You need to leave your house or stand in line, or wander around a store trying to track down a particular title. If you know exactly what you're looking for, you can find it right away.
Digital media is never out of stock or out of print. You don't have hope that a new shipment will come in some day or visit another location, and you don't have to pay exorbitant prices because demand outstrips supply.
Digital media is cheaper to distribute. That means you either get to enjoy a cheaper price, or the content creators get more money, which will enable more content to be created.
There are of course tradeoffs for these benefits. Resale and lending are the common complaints. But the benefits are considerable.

"The worst part about these reviews is they are [subjective]--and their scores often depend on how drunk you got the media at a Street Fighter event." — Mona Hamilton, Capcom Senior VP of Marketing
*Image indefinitely borrowed from BrainBoxLtd without his consent.