A cryptocurrency is a type of currency which is digital in its origins, it makes use of cryptography in order to secure its value and create new units of the currency.
They are also limited entries within the database which cannot be changed unless special conditions are applied.
Some are designed to be decentralized and thus, having no entity to control the amount, production and value of the currency whilst others are centralized thus having entities to control the value of said crypto currency.
In a decentralized cryptocurrency, every single participant takes part in confirming that your transaction is legitimate; this is done by a public ledger that records all transactions that have happened within the network known as the BlockChain, meaning that everyone can see everyone account balance.
Transactions are represented by files that consist of the Senders and Recipients public keys, wallet addresses and amount of currency exchanged. Every single transaction is one that needs to be signed off with a private key from the sender; when this is done, it is broadcasted to the entire network where it is checked by volunteers (Miners) who solve cryptographic puzzles presented by the transaction, once solved, it is saved and confirmed onto the network, legitimizing that the transaction was fair.
Essentially, the legitimacy of the cryptocurrency network is confirmed by the entire consensus of the senders, recipients, and miners. Due to this system of BlockChain, it has been highly trusted with the utmost of safety.