What is the mempool?
The mempool is a special place (data structure presente in all nodes) where unconfirmed transactions wait for a miner to pick them up to add to the next block.
What happens if the miners can’t keep up with the rate of the new transaction?
If the miners can’t keep up with the rate of the new transaction the unconfirmed tx will increases and consequently the waiting time.
How does a growing mempool effect transaction fees?
Mempool is like a market were the miner are competing with each other to pick the tx with the highest fees. Economically, growing mempool means that demand exceeds supply and consequently the price of fees increases (especially for those who want to see their transactions confirmed quickly.)