The Memory Pool, or Mempool for short, is the pool of unconfirmed transactions waiting to be mined by a Bitcoin Miner. Think of the Mempool as an Airport terminal, and all the so far unconfirmed and unverified transactions are people about to travel.
When you click send in your Bitcoin wallet, a Bitcoin transaction is transmitted to the network. This only happens if all the connected Bitcoin nodes verifies the transmitted transaction. In our Airport analogy, when you click Send Bitcoin, the Bitcoin or traveler, enters the terminal. The first thing you do is check-in using your passport, which in Bitcoin Wallet would be entering your Private Key. When you check-in with your passport, the Airport it-system (The Bitcoin nodes) will verify that you indeed are who you say you are, and that you are allowed to travel (that you have balance in your Bitcoin wallet or are not flagged as a flight hazard).
Now you have checked in (your transaction has been verified by the Bitcoin nodes). You have now entered the Mempool. The Mempool consists of all the not yet confirmed transactions waiting to be mined by a Bitcoin ASIC (Application Specific Integrated Circuit) Miner.
Think of this as the scenario when you have gotten your flight tickets but have not yet passed through the TSA agents and entered the gate. In this analogy the TSA agents are the Bitcoin Miners, and the travelers who pass into the Gate are the transactions being included into the next Block on the Bitcoin Blockchain.
These travelers will be be inspected by the TSA agents then they will talk among each other coming to a decision whether they should let you through or not (The Miners will verify the authenticity of the transactions using cryptographic algorithms used to reach consensus among the Miners before they add you to the next Block)
Ironically neither the travelers, nor the Bitcoin transactions are necessarily inspected (Mined) in the order that they got in line. First class passengers (Transactions with highers fees attached to them) will be prioritized. This means that there is no fairness in the Bitcoin network, or the Airline industry when it comes to who is allowed to enter the Gate, or next Block, first.
Once you have been allowed to enter the Gate (Your transaction has been added to the next Block) you are now ready to travel. The Airplane is the decentralized network which makes sure you arrive at the correct destination.
But what happens if the post-check-in, pre-confirmed travelers fill up the terminal?
What happens if too many transactions are added to the Mempool?
If the Mempool's size gets too close to the RAM-capacity of the Bitcoin Nodes which puts transactions into the Mempool, then the Bitcoin Nodes will automatically setup a minimum fee threshold. Transactions with lower fees per KB than the threshold will be rejected by the Bitcoin Nodes and thrown out of the Mempool. In our Airport analogy this would mean that people with cheap airline tickets would be thrown out of the Airport, and not allowed to travel unless they pay an additional fee added to the price of their tickets.