Lightning Network is a "layer 2" on top of "layer 1" bitcoin. The short summary is that it allows two parties to conduct lots of transactions and, when one of them decides they are done, the final balance is committed to the bitcoin blockchain rather than every single one of the transactions. These channels can also be used to forward payments to others, which means that depending on your Lightning node's connections you are able to transact in this way with many thousands of parties beyond just the ones you are directly connected to.
Each channel sets their own rates so the cost of transacting this way varies but it usually comes out to a very tiny amount, much less than 0.1%.
