You may volunteer your men for civil work at any time, to help out rebuilding any infrastructure in the region (under the control of your realm or during a Friendly takeover). This will increase the productivity of the region, and will often carry a morale or loyalty boost with it. However, your men may not like being used as free labour, and their morale may drop if used for civil work for an extended period of time. It is one of the more effective ways to increase loyalty to a realm after a takeover has taken place.
Civil work can not be done when production of the region is at 100%, and can only be done in a single block in a turn (eg. no doing four hours of civil work twice). Also, sometimes you can't do civil work to increase production because the population has decreased and you will have to wait for it to be restored. (No use in rebuilding that mill if there aren't enough people to work in it.)
Doing civil work can increase your honour.