Blockchain are now widely used to perform transactions between two parties where the blockchain ensures the validity of the transaction and records it in the distributed ledger. However, for a transaction to be completed it would require all the individual peer copies of the ledger to be updated. And this can be very time and resource intensive.
The Lightning Network is a protocol that works on tops of a blockchain that allows for transactions to happen off the chain. The protocol allows for a payment channel to be open between 2 parties which is validated by the blockchain. Once a payment channel is set up, all transactions between the 2 parties can happen quite instantaneously. The record of the transaction only needs to be updated in a certificate tied to the payment channel. Once a payment channel is closed, it is recorded in the main blockchain.
An example, a customer can have a payment channel open with a coffee shop and they can use it to pay for coffee everyday. Once the payment channel is closed, say once in a year. The records are ratified and added to the main blockchain.