Cryptocurrencies, like any other currency, represent an exchangeable value.
The “crypto” part refers to the fact that the software uses cryptography. All you need to know is that it is a complex mathematical computation used to securely move the currency from one user to another. Whereas in regular currencies, the process of crediting, debiting and maintaining a ledger of transactions is undertaken by a middle-man, such as a bank, cryptocurrencies use cryptography to create a practically unhackable record of transactions. The record is reflected on a blockchain, which is open, so that anyone can check the assets are being fairly and legitimately moved.
Cryptocurrencies are called “peer-to-peer” because they move between individual users, without need for trust in a third party to execute the transaction. Bitcoin was, in many ways, a response to the loss of trust in banks following the 2009 financial crisis.