The mempool is a data structure found at every node along the blockchain network. It holds all unconfirmed transactions, though in no particular order.
If miners can’t keep up with the rate of the new transaction then the mempool grows in size. Higher fees may occur during this situation and until the mempool shrinks down again.
A growing mempool effects transaction fees by causing them to rise. Miners are looking to be efficient and get as many bytes onto a block as they can; a backed up mempool creates complications for miners, thus higher fees.