Take Venezuela, their currency is/has collapsed because the people no longer have faith that it is valuable.
Typically, people just blindly trust authority, and that's why we believe green paper made from cotton to be valuable. We all agree it's valuable (except people who want a gold standard).
Similarly, we all agree Bitcoin is worth X. It's no different, except no one is telling us it's worth X. The market is saying it's worth X.
It's not really the first time a society agreed to use something arbitrary as valuable either. There are cultures that used salt, gold, silver, white stones, etc. as currency. The point is, once we agree something is worth X, we can trade for other goods at value X.
The advantage to Bitcoin is it's not centrally controlled so it's harder to mess up (see great depression, federal reserve basically made it 100x worse), or Germany post WWI. Further, you have an auditable history, some privacy (better than credit cards), and a truly global currency (similar to gold, without the need to lug it around).