In short:

Fast and cheap monetary transactions without relying on any third parties such as banks or credit card companies.


More lengthy explanation:

Bitcoin enables monetary transactions between two or more parties without relying on central entities such as banks or credit card companies. This works fine if you only have a limited number of users, but gets more difficult the more active users there are. This is because only a limited number of transactions can be handled per second. Lightning Network enables more transactions per seconds by bundling up multiple transactions into payment channels, that is you get multiple transactions for the price of two: Opening and closing a payment channel.


That's as deep as I would get into it without knowing how familiar you are with cryptocurrencies and the scaling debate of the last few months. I hope it gives you a starting point.

If you feel like binging Wikipedia, the Wikipedia page for Lightning Network should give you a rough overview, sprinkled with links to other concepts that you might potentially need to get familiar with:

https://en.wikipedia.org/wiki/Lightning_Network