A cryptocurrency is a digital currency secured by cryptography. A digital currency means that it is used on the Internet, that it is data which sent electronically, to make transactions. The name Bitcoin can be seen as an indicator of this: as such data consists of 'bits' of information. Fundamentally, this means it is payment data which uses the protocols of the Internet, essentially connected networked devices which can send and receive information.
What secured by cryptography means is a little more complex. A core concept in cryptography is hashing. This occurs when a set of data is put through an algorithm or computer program which produces a single string of characters as a unique digital signature of it. A cryptocurrency uses hashing to secure its ledger. A ledger anywhere is a record of transactions. A cryptocurrency typically uses a ledger called the blockchain. This is set of block of data which are connected by hashing. They are more than connected, they are secured from being changed by hashing, as a change in a block, would cascade down the connected blocks. Multiple copies of this public ledger are stored which along with hashing and other measures helps ensure its immutability (i.e. resistance to being changed, after the data has been verified as correct).
Perhaps even more interesting is that to create a new block of transaction data, is a competitive process occurring right now on the Internet, where those who wish to add a block, called miners, compete for the right to this. The reason they do this, is because they get rewarded with some of the cryptocurrency (as an automatic process, like mining an ore) and any transactions fees. When all possible cryptocurrencies have been mined like this (as the supply is normally limited in some way), then they will get paid from transaction fees. Not all cryptocurrencies use miners, there are other ways to process data, not all cryptorrencies use a blockchain structure for their ledgers and some blockchains are private.
So what really is this all about ? Well, it is about having a payment (or other executable) system which has its functions distributed, so no one controls the ledger or database, in a way a central ledger or database is controlled. Rather the ledger is formed and secured by automatic processes, except that humans are involved, but not very directly, as miners use programs to run their mining rigs and help make blockchains. The processes involved in forming the blockchain and verifying blocks are also programs. Humans are involved in computational processes but based on the way the Internet has been designed and programmed, for the purpose of enabling payments and other data to be processed, and rewarded for doing so. That relationship is perhaps where the the novelty (and potential) of this technology may exist.
