Laymans terms...
There is a limit on how many transactions a miner can confirm when they solve a block.
The miner gets to choose which transactions the miner will confirm, and which ones they will leave for a later block.
The miner gets to keep the transaction fees of the transactions that are included in his block.
Given those facts, if you were a miner, would you choose to include the transactions in your block that pay higher transaction fees, or would you choose to include the transactions that won't earn you as much money?
Most miners want to make a profit. That's why they choose to be miners. Therefore, out of ALL the transactions that are waiting to be confirmed, they will typically choose the transactions that pay the highest fee per byte. They will leave the cheaper transactions for some other miner to get stuck confirming later.