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Mempool Depth

A transaction doesn't go directly into a block. First it gets broadcast to the network and sits in a waiting area which we know as the mempool. Every full node has its own mempool and they relay unconfirmed transactions to each other. So what miners do is that they look at the transactions in their mempool to decide which ones to include in the next block and because they are motivated by profit they will prioritize the transactions with the highest fee rates not fee.

Now, the depth of the mempool is a measure of this waiting room's congestion. It's not actually a technical property of a single transaction but more like a dynamic state of the entire network. Imagine the mempool as a long queue with different lanes for different fee rates. The highest paying transactions are at the front and the lowest are at the back. Now when we  talk about mempool depth, we are referring to how many transactions are waiting in each of those lanes.

When the network is congested the depth of the mempool kinda increases which actually means you may have to pay a higher fee rate to get to the front of the line. However if the network is less congested and the mempool is shallow a small fee has a very  high chance of getting you a quick confirmation. This is why Bitcoin transaction fees are not fixed.

Congestion also explains why sometimes the depth you see at the time of broadcasting your transaction may not be the depth the transaction will be confirmed at.