This is a deceptively simple area. Basically for a force you choose both a stance and a level of commitment. Use the buttons to the left of the unit as:
The top row basically tells the unit what to do (Stance). From left to right they are:
Passive-Defensive-Attack-Assault
The second row tells the unit how committed it has to be. Again from left to right:
Passive-Limited-Normal-Committed
The only fixed link between the two is a unit in a passive stance must also adopt a passive level of commitment (ie green-green). The rest you choose as you want (or as much as you can).
Some rough ideas of when to use the different stances:
Passive is great for 4 things:
If you put a force in this stance and it is in supply and on a depot, it will regain losses very quickly (assuming you have replacement chits).
If you use this stance and the unit is in supply, it will regain cohesion very quickly;
If you are marching long distances in safe territory, then this stance will minimise cohesion loss
if you want to avoid combat and/or retreat on contact (say you are falling back after losing a battle) this is a good stance.
Defensive is a bit more obvious. In its favour, you gain from entrenchments and terrain modifiers if attacked. You regain cohesion at a reasonable rate. Against, it, well you don't gain military control over the province you occupy and you can't initiate battle. Also its a posture you can be forced into if your commander is inactive.
Attack, again pretty obvious. You can initiate combat, you don't gain from defensive terrain or entrenchments, you won't regain much cohesion (even if static).
The effect of Assault is mostly in connection with sieges and towns and interacts more with the commitment level you choose. Assault plus either red or orange means you will assault a fortress/city that you end the turn in the same province. This is the only way to initiate an attempt to storm a fort. Be careful, an 'army' stack will not assault unless it is the only stack in the province (so a supply wagon you are sending back to replenish will stop an assault by an army HQ stack but not by a corps). Assault plus red means you can assault forts as you move, so might allow you to conquer a string of weakly defended positions.
Commitment when you are in defensive or attack stances mainly determines how quickly you will look to break off.
So attack (orange) with a green level of commitment means you will try to break off very quickly. Its actually a good combination for a small scouting force. Being an an attack stance means you take military control (which can slow your opponent and interdict supplies) while the green commitment means you have a good chance to avoid too much fighting.
Be careful with the red commitment level (either defend at all costs or all out attack). If you find that you have misjudged the enemy, this can lead to horrendous losses as your troops must fight for at least 2 hours (defend) or 3 (attack).
Usually Defend or attack + normal is a good balance. Your troops will fight, if winning will keep on going, but if losing will retreat to fight another day.
You can check the commitment levels and how long it means you will fight in the GameLogic file.