Command and control (abbreviated "C2") is a unit's communication status within the military command hierarchy. A unit in good C2 will have better morale, and can request artillery from other units in C2.
To be in command and control, each unit must be in communication with a headquarters unit that is part of its command hierarchy. The command hierarchy for a unit is its own immediately superior headquarter unit, plus that unit's superior, etc. For an average squad, that would be its platoon HQ, its company HQ, and its battalion HQ.
Generally, units can only trace C2 to their immediately superior HQ. Higher HQs may provide C2 only to a limited extent. If a unit is out of contact with its immediate superior (usually a platoon HQ) then its company or battalion HQ may provide voice and close visual contact, but not radio or distant-visual contact.
Note that as of CMBN 1.01, C2 provision via higher HQs doesn't happen in campaigns if you lose a platoon HQ. The HQ is not replaced in subsequent battles, and no higher level HQ gives C2 to the now leaderless subordinate. (BFC is said to be working on the problem.)
Communication with HQ
There are two methods by which a unit can communicate with a headquarters unit: visual and audio. A unit has visual contact with an HQ if the units have line of sight to each other. A unit has audio contact with an HQ if the units can hear each other, either via proximity (50m) or via radio. Radio contact is unlike voice or sight in that it has no range or LOS restriction. However, WW2 radios cannot be used when a unit is moving. After a unit stops moving it takes some time to set up its radio and reestablish contact. Also, even for stationary units, radio contact can be lost randomly.
Each type of contact has two levels of effectiveness. Visual contact can work at any range, but it is superior within close proximity -- about 100m. Voice contact is superior to radio.
A unit's currently effective C2 method(s) (if any) are displayed in the Unit Info Panel. The methods are:
Having all methods available to a unit at the same time allows for the best possible results, while having none at all means a break in the chain of command.
Effects of C2
There are three primary benefits of good C2: sharing spotting of enemy units, calling for support, and maintaining discipline.
Units in C2 gradually share their knowledge of the battlefield with each other. (It would be nice to have some research to understand this effect.)
Units require C2 to be able to call artillery and air support. Existing but poor C2 will tend to make the time to get fire high.
Note: On-map mortars can fire indirect even if they are out of command & control and lack a radio, provided that the spotter is within 50m.
For information on artillery in CMBN 1.00, see the article C2 & Artillery. Much of this info is probably still applicable in 1.01.
Lastly, maintaining C2 is important for maintaining unit cohesion. Units tend to get jumpy when they don’t know what the friendly units around them are up to, or where their superiors are, or what the enemy might be trying to do at that moment. Without C2, units are more likely to have morale failures of various sorts. (Research needed here too.)