O_e_l_e_o is good at this and he has been helping me in the simplest method and language ever.
Since I've been tagged, I'll share an analogy I like for explaining the basis behind Lightning in really simple terms below.
Let's say you and I both run our own businesses. Sometimes I buy stuff from you, and sometimes you buy stuff from me. We get fed up of sending money back and forth between our bank accounts (i.e. standard bitcoin transactions), as it is time consuming and the bank charges us a fee every time. So, next time I come to see you to drop off some goods, we get out a jar and both put $100 in it. (Think of this as opening a Lightning channel.) I drop off the goods, and we agree you owe me $20, so we both record that when we open the jar, I get $120 and you get $80. The next day, I need to buy some stuff from you which costs $50, so now we agree that when we open the jar, the split will be $70 to me and $130 to you. This can go on and on for weeks, months, even years, with us both agreeing a new way to split the money, but without actually opening the jar. Changing the balance like this is instant and free. The banks (i.e. the bitcoin network) have no idea this is happening - all they know is that we both took out $100 to put in the jar in the first place. They don't know how we are agreeing to split that money, or how that split is changing.
Next week, I need to buy $20 of stuff from another business down the road. I don't have a jar with them, but you do. So we deduct $20 from my balance in the jar between me and you, and then you give $20 to this other business in the jar that you have with them. You essentially route my $20 to this other business without me having to set up a jar with them, all instantly and for free.
At some point we decide to open our jar (i.e. we close our Lightning channel). At that point we both take out whatever amount of money our final agreement was and deposit it back to our bank account. Only then do we need to make a transaction with a bank (a transaction on the bitcoin network), and only then does the bank/bitcoin network become aware of the final split of funds.