Cryptocurrency is a type of digital currency that uses cryptography for security and anti-counterfeiting measures. Public and private keys are often used to transfer cryptocurrency between individuals.
As a counter-culture movement that is often connected to cypherpunks, cryptocurrency is a new form of value created generally by constrained supply and difficulty of acquisition. Public Blockchains like the Bitcoin and Ethereum blockchains work on consensus with miners. A competitive market is created with rewards in order to decentralize the consensus of the network. When miners agree that the information is true a block is created that stores information, for instance, transaction sends, and smart contract data. You can learn more about blockchains and their history here: https://en.wikipedia.org/wiki/Blockchain