Trust me,you don't need to know anything about the Lightning network.All the hype about super fast transaction speed is exaggerated.The current speed of normal btc transaction is quite good.
Think of LN as a second layer over the bitcoin core blockchain,that's centralized and therefore you don't have to wait for confirmations.It's not the best explanation,but this is how I see LN.
How is the transaction speed exaggerated? You said yourself that there is no need to wait for confirmations. It was designed to facilitate instant transfers. Either way, the Lightning Network is completely opt-in and is mostly meant for point-of-sale and micro transactions. There's really no need to use it if you're not in a rush to send money.
But yeah, the simplest way to put it is that it's just another wallet that has a new network running on top of it. You can effectively transfer Bitcoin outside the blockchain through that network, and you can "save" the changes on the blockchain anytime later through a regular transaction. It's very controversial because it could be argued that it's not Bitcoin anymore, but it does eliminate the need to wait for confirmations, making it more suitable for real world use.