Booting
If a player does not take their turn in a timely fashion, they can be booted out of the game so that the game can continue.
The game creator can set a "boot time" when creating the game that will determine how fast each player must take their turn to avoid getting booted. The boot time typically determines the pace of the game and how long a game will take to play.
Banking Boot Times
Banking boot times is a feature that gives more flexibility to players with the boot times. When banking boot times is enabled, whenever you take a turn under the boot time, you "bank" some of that time. You can then use this banked time to go over the boot time in subsequent turns. The game creator will configure what percentage of the difference that players bank.
This helps keep the boot time more fair. For example, if a player plays very quickly during the week, but not at all on weekends, they don't need to worry about becoming bootable on Sunday evening, even if the boot timer is set to 1 day. Conversely, a player who constantly waits a long time take every turn will become bootable much more easily.
Let's look at an example. For now, let's assume the game creator configured it to bank 100% of the time. If the boot time is set to 24 hours, and Sally takes her turn after 20 hours, she'll bank 4 hours. This means that, for the next turn, she could wait until 28 hours have passed before she'll become bootable. Any time she waits over 24 hours, she eats into her bank. So if she takes 27 hours on the next turn, she uses three of her banked hours and her bank is reduced to one hour.
You can always see how much time a player has banked by opening the nudge/boot dialog and clicking the "speed" link.
The game creator can configure what percentage of the difference is banked on each turn. For example, if the game creator sets the amount banked to 25%, then Sally would have only banked 1 hour instead of the 4 above.
Since banking boot times gives more leeway, it is recommended you use smaller boot times than you would without it. It's also worth noting that only your last ten turns are counted - this means that banked time expires after ten turns. This helps keeps banked time from spiraling out of control in long games.