From the Merriam-Webster Dictionary:
Cryptocurrency “Any form of currency that only exists digitally, that usually has no central issuing or regulating authority but instead uses a decentralized system to record transactions and manage the issuance of new units, and that relies on cryptography to prevent counterfeiting and fraudulent transactions.”
It’s important to understand each piece of the definition. First, it’s digital which makes it mostly software; distributed ledger software (commonly referred to as blockchain) to be specific. Secondly it’s decentralized; which means no central authority controls it. And finally it’s method of security is cryptography.
Prior to Satoshi Nakamoto no cryptocurrency was able to solve the problem of double spending. His famous whitepaper asserting the solution to the problem is still available.
Proof of work mining is what allows Bitcoin to exist as it’s own authority, enforcing it’s own rules through code. In reality most bitcoin miners are simply guessing the answer to a math problem that they cannot solve in a timely manner because of encryption.
Decentralization is part of what gives Bitcoin it’s value because of the assumption that governments and people are corruptible. That money should not be controlled by a central authority but rather an immutable ledger that cannot be easily amended. Trust has always played an integral role in how fungible any currency is. Nick Szabo wrote an extraordinarily informative piece on non governmental money that establishes the historical context for cryptocurrency and Bitcoin.