What it means
A transaction has finality when it is part of a block that cannot change without a large cost to whoever tries. In day-to-day terms, it is the moment you can treat a payment as done. Different networks reach it in different ways.
Probabilistic finality in proof of work
In Bitcoin-style chains there is no moment of absolute finality. Each new block built on top of the one that contains your transaction makes reversing it exponentially less likely, because an attacker would need to redo all that work. That is why people count confirmations: six on Bitcoin has long been a common benchmark for large payments, though the right number depends on the amount and the chain's hashing power.
Economic finality on Ethereum
Ethereum's proof of stake adds an explicit finality mechanism. ethereum.org explains that a transaction has finality when it is part of a block that cannot change without a large amount of ETH getting burned. This happens when checkpoints receive votes representing two-thirds of the total staked ETH. Reversing a finalised block would require an attacker to put a huge amount of staked ETH at risk of destruction.
Why services care
Exchanges, bridges and merchants decide how long to wait based on finality. A bridge that mints a wrapped token on another chain wants the original deposit to be final first. A merchant selling goods wants more confirmations for a larger sale. If a service asks you to wait for a number of confirmations or epochs, it is waiting for finality.
What you should do
Wait for finality before taking irreversible actions that depend on a deposit. For small amounts, a few confirmations may be enough. For larger ones, follow the platform's published requirement and do not hurry because an interface shows a pending status that looks complete.