Honest to goodness, I don't remember the last time I did any kind of exchange of actual cash. Everything I do is digital - or online, if you prefer. I adopted online use because of how convenient it is, and how much easier it is to keep track of.
Now, if by "digital money" you're talking the likes of Bitcoin, then that's a whole other matter.
Back in Ye Olde Days, we had the Gold Standard. Essentially, the value of a countries money was represented by physical gold which was held in vaults. There was a physical connection between all the money, and it's golds holdings. That went away early 20th Century with the World Wars and Great Depression. The whole thing changed, and today we have fiat currencies. The value of our money is essentially governed by the exchange rate against other currencies - there is no physical link to Gold. The amount of currency that exists is decided by each government (centralized).
Bitcoin isn't not a decentralized, in that it does not belong to a specific country. In very very simple terms, think of Bitcoin as a set of shares. There is a finite number of shares, and that gives the shares a value. People buy and trade shares as they see fit, and realize that value (or indeed, lose value). Since Bitcoin is finite (at the time of buying) it also has value in terms of traditional money. Hence, it interacts with real money (as it were). There is a global ledger of all Bitcoin transactions, which is known as "Blockchain technology" - it records every single Bitcoin transaction (it's not kept in one place, it's decentralized).
All of that said, I'm not in Bitcoin. I know my brother lost a lot of money in it, but like everything else, you have to understand the market.
