When you have scattered your foes in battle, you are unlikely to want them to get away -- after all, they'll just reform and attack you some other day. If your unit is large enough and your unit was not itself driven from the field of battle, you may hunt down your scattered and retreated foes and attempt to apprehend them.
This is by no means a safe or easy activity. First off, you'll need to spend three hours -- this is for selecting men for the hunt, and equipping them for it, and poring over maps of the region and reports of the battle to figure out the best strategy to hunt those dogs down. Even with the three hours spent, you'll need to wait for the turn (when the hunting parties report back) to see how things fare.
At the turn, your parties will report in. Sometimes they'll have had no luck. Sometimes they'll have cornered a few enemies and captured them. Often, the enemy troops will put up a fight, and your own men are not guaranteed to win: desperate men can fight like lions, or lay cunning ambushes.
Because of the nature of the task, anything that requires your men to participate (such as digging in, or travelling to another region) will call off the hunt, wasting the time you've already spent planning.
Deciding whether to hunt is a decision that needs careful attention. You want your hunting parties to be as large as possible, so that if they find the foe they easily overwhelm them and convince them to surrender.
A hunting party can be as large as 26 men (and perhaps larger). So for instance if you currently have 25 men in your unit, then it would be a good time to hunt as you'll have only one hunting party with your entire unit in it.
Larger than 30 or so and your unit divides into multiple parties. This gives you a better chance to catch the enemy (in theory, needs to be confirmed), but it may also make your hunting parties individually weaker. For instance, if you have 37 men, then you might end up with one hunting party of 16 men and another of 21 men (they're not usually of equal size for some reason).