LN allows two parties to transact between each other without having to make an on chain (and thus costly due to fees) transactions for each transaction that they want to perform. If two people were to make 5 transactions on an LN channel, instead of paying 5 transactions worth of transaction fees, they would only need to pay 2 transactions of transaction fees (opening and closing transaction).

Two people decide to make a LN payment channel. They make a transaction that sends Bitcoin to a 2-of-2 multisig address. Then they make another transaction which spends from the multisig address and sends Bitcoin to their own addresses. This second transaction is not broadcast. When one person in that channel pays the other person, they remake the second transaction and change the amount that their address will receive. Again, this transaction is not broadcast. They repeat that step as long as they want. When both people decide they no longer want to continue transacting with each other, the last transaction that they had created will be broadcast to the network and they will receive the Bitcoin back to their addresses to be used elsewhere.

LN transactions don't touch the blockchain until the channel is closed.

Channels are opened by both people in the channel sending some amount of Bitcoin to a 2-of-2 multisig address. Channels are closed by broadcasting a transaction which spends from the multisig address and sends some agreed upon amount of Bitcoin back to the addresses of the people in the channel. If any payments over the channel had occurred, then when the channel is closed, both people will likely have a different amount of Bitcoin coming out of the channel than they had put into the channel.

Miners and nodes are not directly involved in LN. However there can be LN nodes, i.e. people who have lots of channels open with other people so payments can be routed through him.

LN is one specification of a payment channel network. There can be others as well, and you can have LN payment channels without actually being connected to any other channel in "the network".

LN transactions are still Bitcoin transactions.

Makes sense. More straightforward than I would have guessed. It is basically a blockchain tranx that enables 0 time exchange of coins that both parties signed off on instead of the network signing off on the transx.

Is there any interest in applications that have LN enabled that parties can make an agreement based on set conditions lined out? Similar to smart contracts on ETH, but instead of the blockchain enforcing the contract, the LN regulates the conditions. When both parties sign the contract(actually sign each condition met,) then coins are exchanged. Correct?

What about "multi-party" transactions. Say I want to send 1 BTC to Alice, Bob, and Charlie. 0.4 to Alice, 0.5 to Bob, and 0.1 to Charlie. The current implementation does not allow this does it? Could this be alleviate with multiple keys signing off on my transx with a contract? Of course, if one of the third-parties refuses to sign, then the transx cannot commence, unless conditions say otherwise.