TL;DR: The purchase pool is the running total of coins you hold per currency (and, if Depot/Lot separation is enabled, per exchange/wallet). Buys, income, gifts and mining add to the pool; sells, donations and spends remove from it and trigger a capital gains calculation. Deposits and withdrawals are just internal pool movements and don't change the pool size or cost basis on their own, but a deposit does carry over the cost basis of the original buy through the transfer, so it isn't lost. The order in which coins are taken out of the pool depends on the accounting method you choose (FIFO, LIFO, etc.).
What is the purchase pool?
The purchase pool is the pile of coins you collect in the background. Added to it are coins from trades, income, gifts and mining with their respective asset value from that day. Taken out are sales, donations and spends, all of which trigger a capital gains calculation.
The sequence by which coins are taken out of the pool depends on the method chosen (FIFO, LIFO, etc.).
The crucial point is that a deposit does not add to the pool and a withdrawal does not reduce the pool. They are "internal pool movements" with no consequence on gains or taxes.
So if you enter just a deposit for a coin, this coin is a "ghost coin" with no value. It will show up on your dashboard total, but not in the pool for the tax calculations. When it is sold, a warning appears in the tax report and on the gains page.
The purchase pool is based on transactions. Buys or Income fill the pool, and sells or expenses reduce it, and if you use depot separation (Depot/Lot separation) those pools are logically built for each exchange. Without the depot separation filter there would only be one pool per coin for your whole account.
So if you buy 0.1 BTC and later again 0.1 BTC, which leads to a pool ("pile") of 0.2 BTC, and you sell then later 0.05 BTC, you have a pool left of 0.15 BTC. If you were to miss adding both buys and only add the sell, you would receive a purchase pool warning across the reports. To check what is wrong, please use the reports described here: How to validate my account?
How does a deposit carry over the cost basis of the original buy?
Even though a deposit is just an internal pool movement and doesn't add a new cost basis by itself, the coins arriving via a deposit keep the cost basis of the original purchase. In other words, when coins are withdrawn from one exchange/wallet and deposited into another, the original buy price (and date) travels along with the coins through the transfer. It isn't reset or lost. This is what allows the purchase pool to correctly calculate gains later, even after coins have moved between multiple exchanges or wallets, as long as the corresponding withdrawal and deposit transactions are entered and matched.
When is the cost basis actually relevant or visible?
If you are not using Depot/Lot separation, there is only one pool per coin across your whole account, so the cost basis of individual buys isn't tied to a specific exchange. In this case, the cost basis only becomes relevant (and visible) at the moment of sale, when the chosen accounting method (e.g., FIFO) determines which buy(s) are matched against that sale in the capital gains calculation.
If you are using Depot/Lot separation, pools are built per exchange/wallet, so you can trace the cost basis of coins as they move between accounts, not just at the point of final sale.
How can I trace the cost basis of transferred coins across exchanges?
If you use Depot/Lot separation and want to see how a specific coin's cost basis moved from one exchange or wallet to another (e.g., after several transfers), you can use the Transaction Flow Report. It lets you trace the path of transferred coins step by step, showing how deposits carry forward the cost basis of the original buy across exchanges, which is especially useful for verifying gains calculations when coins have passed through multiple platforms.
Why is the transaction amount on the tax report page possibly different vs. in the tax report itself?
On top of the tax report page, the real transactions are counted for the tax year (picture 4422 transactions).
In the capital gains report, which is part of your tax report, each real transaction can be split due to purchase pool consumption, e.g., if some parts are "short" (holding period) and others are "long", more transactions are listed in the capital gains report, which you can check in the detailed calculation report. Therefore, there are normally more transactions listed here (picture 7272 transactions).
There could be a difference as well due to the group by day option. For the license calculation, only the real transactions are counted.
Further information on purchase pool warnings
"There is no suitable purchase to this sale (all purchasing pools consumed)"