They're a breakthrough in Computer Science and enable different use cases for digital payments e.g., machine-to-machine payments. You're trusting mathematics and code and not trusting any entity. Future of cryptocurrencies is a broad topic, hard to answer it here. I'd recommend watching some TED talk on this; Neha Narula has a good one https://www.ted.com/talks/neha_narula_the_future_of_money