It is a second layer protocol on top of Bitcoin that defines rules and contracts which enable the fast, secure, private, trustless and permissionless transfer of Bitcoin.
Like a standard Bitcoin transaction, a payment on the Lightning Network can only be refunded by the recipient.
While all Bitcoin transactions are stored in the blockchain where they can be tracked, the payments on the Lightning Network are off-chain and offer more privacy than Bitcoin payments.
Due to the use of onion routing, which is also used in Tor, even the nodes that are involved in forwarding the payment from the sender to the recipient do not know for whom they deliver the payment.
* first response by James A. Donald on the cryptography mailinglist to Satoshi Nakamoto: https://www.metzdowd.com/pipermail/cryptography/2008-November/014814.html "We very, very much need such a system, but the way I understand your proposal, it does not seem to scale to the required size"
John is a 9 year old boy from Australia, who wanted a games console just like his friends. However he was told by his dad that in order to buy it, he had to earn the money by himself. Now John is an aspiring artist so he knows that while he is still learning, he can't charge much for his artwork. After learning about Bitcoin, he managed to setup a website to sell his drawings across the internet. By using the Lightning Network, John was able to charge as little as $1 for one of his drawings. By being able to set a fair price, which would normally be considered a micropayment and as such not possible with other payment methods, and by using a global currency such as Bitcoin, John was able to sell his art work to customers all over the world and in the end buy the games console he so very much wanted.
A person who wants to earn interest on their bitcoin without the risk of lending them to other people could decide to set up routing nodes on the lightning network.
By providing liquidity to the Lightning Network the routing capacities will be increased offering the chance to earn routing fees on the owned bitcoin.
Silke runs a small coffee shop in an upmarket street in Berlin.
She knows about Bitcoin and wants to accept it in her shop, but has been reluctant to do so because she knows that Bitcoin payments take approx. 10 minutes to be confirmed into her account.
However with the Lightning Network, she knows that her regular clients, such as Joerg can pay for their coffee at her shop, quickly and with negligible fees.
Additionally, by using the Lightning Network, Silke has all funds deposited instantly to her wallet and with usually smaller fees on her side as well.
Ultimately this allows her to provide a better service or to offer better pricing for her products.