Crypto-currencies are a new form of currency that utilizes a publicly verifiable open ledger.
They require little or no forms of identification to set up an account and are used to transfer tokens of value around the globe.
The advantage of using a crypto-currency instead of a conventional system of transfer of value like Paypal is the fact that you are not subject to a third party controlling your funds in any fashion or limiting your money.
All transfers are done and final, which means you will never be subject to a reversal of transaction.
In addition, you maintain complete access and control over your money and a third party will not be able to encroach upon it.
Once you have access to your funds - it remains yours as long as you keep your wallet secure.
We recommend you read the following article to understand crypto-currencies in detail