What are Crypto Currencies?
As per wikipedia, A crypto currency (such as Bitcoin, Litecoin, Feathercoin, etc.) is a peer-to-peer (p2p), decentralized, digital currency whose implementation relies on the principles of cryptography to validate the transactions and generation of the currency itself.
Let us look at the first sentence again and break it down on word for word basis:
Peer-to-peer refers to each node on the network being able to connect to any other node and act as both a server and a client sharing updates to the blockchain (public ledger) without the need for a central server.
Decentralized refers to the peer-to-peer architecture of the network. Because each node can act as both a server and a client, there is no need for a cenral server or centralized authority. Effectively solving the double spending problem.
Digital currency, among its various names, is electronic money that acts as alternative currency in the digital realm (though now a days offline adoption is increasing as well). Currently, alternative digital currencies are not produced by government endorsed central banks nor necessarily backed by any national currency.
Principles of cryptography
Cryptography relies on public and private keys for security. With crypto currencies every transaction has to be signed by a private key for security. Due to the strong security and well understood principles of cryptography counterfeiting digital currencies is virtually impossible.