What is cryptocurrency?
Cryptocurrency is a completely digital, decentralized form of currency. It can be used as a means of payment or exchange (though that's not a very practical use today), or as a potential store of value. Since it's a digital currency, you can't carry Bitcoins around physically in bill or coin form; all transactions take place online. Cryptocurrency is also decentralized, meaning it's not backed by government authority the way the U.S. dollar, for example, is. Instead, it's maintained by its users.
What is the purpose of cryptocurrency?
The original intention behind Bitcoin, the first cryptocurrency, was to create an electronic cash system people could use in daily transactions. You technically can buy and sell things with it, but Bitcoin's price fluctuates quickly, which makes it a poor fit for spending instead of cash. You could spend $50 worth of Bitcoin on something today that ends up being worth $20 tomorrow. It's also not widely accepted as a form of payment yet, so you'll have very limited purchasing power.