Game creators can choose to allow attacks by percentage instead of fixed army numbers.
When this is enabled, a new option appears under the Advanced menu of the attack/transfer dialog labeled by percentage. When checked, the attack/transfer order will be issued based on a percentage of the available armies to attack with instead of a fixed number.
This is most useful in multi-attack games, so it's recommended to enable this setting if you also enable multi-attack. Outside of multi-attack games its uses are limited.
In multi-attack games, all attacks default to percentage mode.
The percentage is applied to the total number of movable armies when the attack occurs. Therefore, if you want to split a stack equally between two attacks, you should first issue a 50% attack order and then a 100% attack order.
For example, say you have a stack of 41 armies and you issue a 50% attack order. One army must always stay behind, so 40 armies are movable. 50% of 40 is 20, so 20 armies will attack.
21 armies remain on the territory. If your second attack also says 50%, only 10 of the remaining 20 armies will attack. Entering 100% for the second attack causes an even split, 20 and 20.