I didn't 'get' it for the longest time. But I moved from one country to another, and I didn't want to bring all my paperwork around with me. So I bought a scanner which can scan duplex (both sides), and a red stamp which says 'Scanned'. I digitized everything except super important things like (birth cert, etc). Tagged it, and it sits in Evernote. I've been in many situations where I am at a business or company, and someone asks for X document, and expect I have to leave to get it, but I can whip it up on my phone and mail it to them if needed.
I scan my bills, and the payment receipts, etc. I keep copies of paystubs, etc.
When I start projects I make a new folder under my existing 'Projects' notebook, and I can put everything related to it in there.
With premium, it also scans through the PDFs and can help you find things when you need them. Again, I know not everyone can afford it. Just pointing out that, if you are in a position where you can, and you could use this kind of functionality, I find it super helpful.
Last tip, use the 'Scannable' app (iOS at least). You can scan documents (very well, surprisingly!!) on the go. For example, once I got roped into signing a new contract for a phone plan. I didn't want to carry all the paperwork around all day, so at lunch I used scannable to send it all directly to my Evernote, and shredded the originals.
Not affiliated either, just a fan who likes the software.