The basic unit of the Lightning network is called the payment channel. This is a private conversation between two users that enables the exchange of cryptographically enforceable IOUs. As long as both parties follow the rules, there's no need to broadcast these individual transactions to the broader bitcoin network. In principle, two parties can make dozens, hundreds, or even thousands of payments to one another without cluttering up the blockchain.
In the Lightning vision, the old-fashioned bitcoin network becomes a cryptographic backstop for these payment channels. The IOUs are actually cleverly-formatted bitcoin transactions called commitment transactions that haven't yet been submitted to the bitcoin network. A user always has an option to "cash out" by posting the current commitment transaction to the blockchain and collecting the money she's owed.
But payment channels aren't enough to solve bitcoin's scaling challenges on their own. In the real world, people want to make payments to a lot of different people—including a lot of one-off payments to people they're never going to interact with again. Each payment channel generates two bitcoin transactions: one to open it, and a second to close it. So if people had to open a new payment channel to every recipient, congestion on the blockchain might get worse rather than better.
So the Lightning network provides a cryptographically secure method for chaining payment channels together. If Alice has a payment channel with Bob and Bob has a payment channel with Carol, then Alice can pay Carol by sending some money to Bob and asking Bob to forward the money on to Carol. Crucially, the Lightning protocol guarantees that Bob can't steal the money as it passes through his hands.
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