Everyone has a secret or two. But if you need to share that secret with someone without others being able to know then you'll need a cipher. Essentially you need to make it so that only you and the persons you wish to share the information with can understand the message. That's the essence of Cryptography.
Over the centuries various methods have been developed to make understanding of secret messages much more difficult. Today we have computers and dedicated hardware which makes the decryption methods nearly unbreakable. The thing is that nothing is totally unbreakable. Remember the idiot proof box? When someone comes up with it then a better idiot will come along to muck it up. That's just the way things work. Everything is in a constant state of evolution and as such what's unbreakable today will be simple for a youngster in the near future.
Crypto-currencies are electronic currencies based upon cryptographic encryption methods. Currently there are close to a dozen different electronic/crypto-currencies in use. The largest two are bitcoin and litecoin. One uses the SHA-256 encryption algorithm and the other uses the SCRYPT encryption algorithm. You can learn a great deal about each by performing a simple google search so I'll not bore you with the details.
Each "coin" attempts to address various features and/or weaknesses of a particular "coin." For example litecoin is designed to prevent hardware specialization which is currently being performed via bitcoin farms. It does this by utilizing a memory intensive algorithm that makes hardware optimization much more unrealistic/unlikely. That's not to say it cannot be done. It's just not a very simple process.
We believe that the various electronic currencies have a place that allows businesses and individuals to operate on a worldwide market without the hassle of financial middlemen. You can find many references to very similar statements throughout the crypto-currency movement. Feel free to ask questions and we will help clarify any questions or concerns you may have.