Before we actually understand crypto currencies, its very important to first understand Blockchain which is the building block for Cryptocurrencies
Even before Bitcoin was introduced in 2009 by Satoshi Nakamoto with its white paper introducing Blockchain, many attempts were made to introduce digital currencies. However, none of them ended to be successful as nobody was able to figure out the right mechanism to maintain a real time ledger to manage these currencies, without an intermediary.
Satoshi Nakamoto was able to address this aspect with the introduction of BLOCKCHAIN, which essentially became the genesis or backbone of Bitcoin.
Satoshi introduced Bitcoin in 2009 after finding unfair treatment to taxpayers when their money was used by a centralized authority, US Federal Reserve, to save various financial institutions on Wall Street. His genesis of introducing Bitcoin was to have a decentralized currency which is completely controlled by the people and does not have a centralized authority. A crypto currency is not backed by a single government or indeed any single organization, it is indeed backed by the miners or people who contribute resources to making the distributed ledger system work for the crypto currency.
And subsequently, 700+ crypto currencies have been introduced which are solving various different problems which leverage the blockchain technology.