Their rarity is what makes them valuable and the fact that they can easily be used for electronic transactions.
It takes extremely powerful computers and a significant amount of electricity to create a Bitcoin but anyone, who is capable and willing to make the effort to do so, can create a new Bitcoin. This makes Bitcoins difficult for the statists who want total control over currency and total control over all financial transactions.
Ie, they are only backed by faith. A lot of things are rare, it doesn’t make them currency. At least though, most rare things are tangible. Bitcoins aren’t. Heck, even if you strip the monetary value of a dollar, it has some value as paper. Bitcoins are just blips of data in the ether.