It's not that these things are basic to the nature of money. Far from it. But these concepts are inextricably linked with money, and it takes a lot of conscious effort to separate them from the useful and important things about money. Fundamentally, money is a medium of exchange, a system of carrying information about value. Money is important because it allows two people to trade even if only one of them has something the other wants.
Money becomes the value placeholder for such exchanges.
But money itself has no intrinsic value, its value is derived from the degree of trust that it can be used to acquire the things you want. Another reason US currency is trusted is that it is legal tender. So everyone in the US is forced to trust the value of US currency. The combination of the fact that almost everyone trusts it and that it can acquire almost anything makes our currency system extremely powerful. Until this century, US currency was trusted for another reason, it was backed by gold.