For a bank transaction such as a purchase there are several events that take place, but the two we care about is the authorization and the settlement.
The authorization hold (sometimes called the pre-auth) notifies a bank that a specific amount needs to be set aside to secure a transaction. For a restaurant purchase the authorization is typically the cost of the meal.
When the final amount clears (called the settlement) this notifies the bank of the final approved amount. This is the amount that is actually taken from the account, which might be higher or lower that the authorization hold. For a restaurant it might be higher since the settlement would include the tip as well.
If the settlement is higher, then the additional is taken out. If the settlement is lower (or the transaction is cancelled) then less will be taken out and the hold is removed. Holds can last up to 30 days, but typically are only on an account for 1-5 days before the settlement amount is processed.