First of all I want to mention that the Lightning Network is very komplex in terms of technical aspects. I am focussing on the easier basics which you really need to know.
The lightning network makes it possible that 2 users can send bitcoin to each other instantly (that´s why it is called LIGHTNING network) and without anyone else protocolling this transaction.
This is possible, because the 2 bitcoin users have to open a "payment channel" and therefore tell the miners how much money they can store in this channel. When the payment channel is opened, the two users can send bitcoin instantly through this channel. if they have transactions to another person, they have to use the regular way of doing this.
The only thing important for the bitcoin blockchain is who is in the payment channel and how much money is in this payment channel.
the money in the payment channel gets sort of "locked" and can only be used in this payment channel.
If the two users decide to close this channel, they have to tell this the miners by telling them their individual balance of this payment channel.
because there are only 2 people in this channel, there can be no (or only a very little chance) of fraud. The miners check if the sum when opening the channel stayed the same until the closing of the cannel. the sum is calculated with both balances of the two users.