Well, what gives the money in your wallet value? The short answer is: currencies have value because people decide to value them. Most people use money without understanding it; money is just part of our social environment. The whole thing is easier to visualize if we use gold as an example.
Gold had very little practical applications before computers became a thing. However, gold was rare, and it was subjectively very beautiful. For a society that barely has candles, seeing polished gold shine under sunlight was quite the spectacle. It made people covet gold, many societies even considered it sacred.
Because people wanted gold and there wasn’t a lot of it, gold became a tool for trade. It became a currency. Cryptocurrencies are the same way: people want them, but the amount of currency available limited by design. The mismatch between supply and demand causes dollar prices to skyrocket.
Why people want cryptocurrencies is an even more complicated issue. Some just see it as a speculative investment, others think this technology will make banks obsolete. If you’re curious, you can learn more from VanillaCrypto at https://vanillacrypto.com.