"Money is a database for resource allocation"
I think I have a pretty deep understanding of what money actually is on a day to day basis because of Paypal...
...think of money as information. People often will think of money as having power in and of itself. It does not.
Just think of money as a database for resource allocation across time and space.
And then in what form should that database or data system — what form would be most effective? You're operating an economy and you need to have something that allows for efficient value ratios between products and services. You have this massive number of products and services and you can't just barter, that would be extremely unwieldy. You need something that gives you a ratio of exchange between goods and services and then something that allows you to shift obligations across time."
This is from an interview Elon Musk did with Lex Fridman in 2021. Elon has said something like this a few times. Predictably, he gets crap for it.
"Billionaire Elon Musk calls money 'Just an entry in a database' as fortune continues to soar." - The Independent
"Only the world's richest man can say money has no power!" - Twitter
What this means
When Elon says, "money just an entry in a database" he's not saying it in the way people say "age is just a number" or that if he logs into his Chase checking account and sees a $142B balance that that number is in some database on Chase's servers.
Instead, what I think means is that anytime you buy or sell something (or steal, or give), what you're really trading is resources. Money (technically prices) is information about these resources relative worth.
So as I write this, the idea of money as information allows me to say one bushel of wheat ($8.61) is worth 2.7 gallons of gas (at $3.15 per gallon), or 29 minutes of an Amazon warehouse employees time (at $17.84 per hour).
These are the ratios of exchange between goods and services that Elon is talking about.
Time and Space
Like Musk says, the money db is necessary to move value across time and space.
If I grow some tomatoes, those are ripe, juicy resources, ready to consume now. They're not going to last forever. But I can "sell" them to you, i.e. trade for money.
How does the money paid for tomatoes relate to value?
One answer is the value of money >= tomatoes for me (since I sold them) and money <= tomatoes for you (since you bought them).
But again, because money doesn't have any value in and of itself, we're really comparing the resources we can buy with $5 to to the tomatoes.
Moving value across space is a pretty easy extension of value across time. Unless I sell my tomatoes then literally stand in one spot (maybe waiting for a food truck drive by or something?), any shift in value across time is also a shift across space.
Is it really a database?
Although I think it's catchy, calling it a "database" is a bit misleading. It's not a database in the sense that it's persistent. If you pay me $5 cash for a carton of tomatoes there's no record of that anywhere. Musk's alternative framing, that "money is information" is probably more accurate.
Also, the information we get is one particular facet, namely the marginal value of the resource. Marginal basically means "the next". Right now I have a house, with running water + a bunch of seltzers in the fridge. That's all very relevant for how I value a marginal bottle of water I might buy from the store (not that highly).
Marginal value (or cost) exists on the producer side too. Each bottle of water costs something to make. If I need to build a giant water purifying plant, maybe the first one costs a lot, then they get cheaper after that. Maybe eventually (depending on how many I'm selling and where "the next" is) they get more expensive as water becomes harder to find.
The point is, a price as an entry in the money DB is at a very specific and context dependent point (the margin). It doesn't tell us e.g. the total value of all the water on earth and let us compare that to the total value of diamonds.
If you think about it, this makes sense. The value of something (even in terms of other resources) very much depends on how many you already have + what else is going on.
The software behind the money database
Musk thinks of different monetary systems as sort of the "software" this database runs on. The current, US government as money supply system (in practice a lot banks/credit card companies running "COBOL in batch mode") works pretty well.
Historically, one problem with government as money database is that, as Musk says, "governments [dilute] the money supply as a pernicious form of taxation." I.e. governments have political incentives to print money. That's because people like government spending a lot more than they like paying taxes, and why some people advocate e.g. a gold standard.
Cryptocurrency like Bitcoin could be another alternative. But it has drawbacks too, probably ones more serious than the risk of government dilution. As Musk says:
There is a fundamental issue with Bitcoin in its current form in that it's transaction volume is very limited. The latency for a properly confirmed transaction is too long. Much longer than you'd like. So it's not great for a transaction volume standpoint or a latency standpoint. So it is perhaps useful to solve an aspect of the money database problem, which is a store of wealth or an accounting of relative obligations, but it is not useful as a currency.