I think the basic idea of lightning network is in and out between 2 accounts, but this can be generalized to much more, even if there is no transaction between to btc addresses. This is just a record of some transaction that is then sent to the blockchain. It's like if you sent btc to a A address, that send the same amount to the B address that finally send your btc to the receiver address. Then all transaction that have used the virtual A/B addresses goes to the blockchain. Note that A and B addresses can be used as sender/receiver, and the blockchain has just to receive the sum of these transaction. So you just send btc to someone, he receives it instantly thanks to lightning network, and ultimatly the blockchain record it. No idea of what you see about your address on the blockchain, maybe some transaction labeled as lightning.
So, yes, it is a scalability solution, this plus bigger blocks, maybe to handle all information about the transaction of a lightning network (that have to be recorded) will make BTC the more powerful crypto by far. Just add smart contract and you have a beast that no one can beat ...
I'm not a blind BTC believer, just realistic, my favourite crypto that I hodl wathever is LTC (just saying to be clear).