I have $10 worth of lunch, I eat it, it's gone
I have $10 in cash, I spend it to buy a lunch and eat it, it's gone too. But, that $10 note now becomes the income of the restaurant, they will spend it later, which will cause another $10 income for another guy, and so on...
In the first case, I ate a lunch, did not create any other economy activity
In the second case, I still ate a lunch, but I created a serial of economy activities
Why such a big difference just because the existing of currency? Is there something fundamentally different in the currency than general goods/services?
In both cases, every party produced $10 worth of value, and consumed $10 worth of value.
In the first case, there is only one person, and that person created a $10 lunch, and then consumed it.
In the second case, you have to keep in mind that the chain is infinite in both directions. You got the $10 from someone by trading a similar value for it, and they got it from someone else by the same system, and ditto for the lunchmaker, and the person the lunchmaker trades with forever into the future.
The chain is also virtual, since commerce is really a web, not a chain. A few threads may break, but the overall web goes on forever.
Money is just a way to virtualize barter. Rather than trading wealth for wealth, you can trade wealth for a claim to wealth, and later redeem that claim. Now virtualized, trade no longer needs to be atomic. The giving and the receiving can now be done at different times, and between different parties.
Of course, this is just a metaphor. Trade is still atomic, you still give and receive at the same time, and with a single party. But the widespread acceptance of money allows you to act as if the metaphor was real.