The reason it's so hard for most people to understand Bitcoin is that most people don't really understand money. Money isn't wealth. It's an accounting system used to facilitate the exchange of wealth. (The paradox of money is that while everyone wants it, no one actually wants it - they want the stuff they can buy with it!) Many people are put off by the fact that Bitcoins are 'just data'. But that's what ALL money is, information! More precisely, money is a means for credibly conveying information about value given but not yet received (or at least not yet received in a form in which it can directly satisfy a person's wants or needs).
To put it yet another way, money is a ledger. With fiat currencies like the dollar, that ledger is centralized. And that gives the central authority responsible for maintaining that ledger tremendous power, power that history has proven will inevitably be abused. With Bitcoin, the ledger is decentralized. And that means that no one individual or entity has the power to arbitrarily create new units (thereby causing inflation), freeze (or seize) your account, or block a particular payment from being processed. We've had decentralized money before. After all, no one can simply print new gold into existence. And the 'ledger' of gold is distributed because the physical gold itself (the 'accounting entries' in the metaphor) is distributed. But with gold, that decentralization comes at a heavy price (literally). The physical nature of gold makes it hugely inefficient for global transactions.
And this is why Bitcoin is important! It is the first currency in the world that is both decentralized and digital. It is more reliably scarce than gold and more private and transactionally efficient than "modern" digital banking. This is why people are excited about Bitcoin, it has the potential to be completely revolutionize money.
Actually, our current system isn't too far off from being totally digital, the only people standing in the way are those who refuse to accept digital money transfer. I never see 90% of the money I earn every month in anything other than a number. That too is protected by a much smaller but still existent form of decentralization, namely that all the banks in my country that my money passes through check with each other to make sure that the money being sent is correct.
None of these concepts are new, the only new thing is that states no longer have authority over the currency itself. Fiat currencies primarily have value because people use them for economic activity. We can see this value too in gold and silver - (it isn't so much about countries, it about people in general attributing value to something). When it comes to Bitcoin, people see the value because it enables economic transactions that weren't possible to do before Bitcoin came along. Combine that with the very limited supply of Bitcoin, then it is no wonder why each Bitcoin goes for thousands of dollars. So as with everything else of value, Bitcoin has value because people believe it does (and then proceed to use it).
People are putting way to much weight in the role of government when it comes to economic activity. Economic activity can happen (and has happened) in places where there is no government and no need for government currency! Let's take a different approach. Think about how a commodity is valued. People attribute value to any given commodity because of the unique use cases it enables - wheat, coffee, copper, cotton, etc (has pretty much nothing to do with governments - after all, these things will have value to people regardless of what any government might say). Think of Bitcoin as a new type of commodity - a digital commodity - and all transactions that happen using Bitcoin as a barter transaction (trading this for that). It should become clear that trading commodity A for commodity B doesn't need any government at all attributing value to them! So what you need to realize that at the most fundamental level, it comes down to PEOPLE engaged in economic activity that give things their value (NOT GOVERNMENTS).
Some people have a narrow view of things because they only know the comfort of their first world couch. But you need to look at what is happening in third world countries. For example: there are many news stories about how people in Venezeula are using Bitcoin to bypass the corrupt government capital controls. A good example of how Bitcoin is solving real world problems.
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