Following is a quote from the developers:
A corps commander uses his leadership skill to boost the chance of a division in reserve entering combat if space is available and any trait bonus is passed to the relevant divisions at 50%.
We have talked a bit about units and leaders already. However let’s
just do a recap. The base structure of a land unit is a brigade, the
smallest tactical unit is the division that is made up of one or more
brigades. Units can be structured into a hierarchy of corps, army, army
group and theatre. Each level can have its own commander with its own
bonus.
Now for a bit more detail. First off we have added rank limitations to
each level. So Divisions are commanded by Major Generals, Corps by
Lieutenant Generals, Armies by full Generals and Army Groups and
Theatres by Field Marshals. Next to bonuses. Commanders have a
leadership skill and sometimes traits, in Hearts of Iron 2 these were
used by all units in the stack and in the case of leadership skill
applied in combat. So first up the division, each division commander
gives a combat bonus to his division based on his skill and any trait
bonus is received 100% by the division he commands if it applies.
A corps commander uses his leadership skill to boost the chance of a
division in reserve entering combat if space is available and any trait
bonus is passed to the relevant divisions at 50%. The bonus is passed
to each eligible unit, the total bonus is increased by leader skill and
radio strength of the unit and decreased by distance from the Army HQ.
The more effective the radio communications of an HQ is, the better the
HQ is and the easier it is to detect by SIGINT.
Army commanders aid organisation of all units under their command. The
bonus is passed to each eligible unit, and the overall bonus is
modified in the same way as corps, however an army commander has a
longer range, the trait bonus is halved again.
Army Groups assist with logistics. All units under the command of an
army group have reduced supply consumption. Again it is modified in a
similar manner but has an even longer range than army commanders. The
Trait bonus is halved yet again. Finally the theatre commander, he
reduces the effects of the unit cooperation penalty for multiple
brigades and is not modified by range. The theatre commander’s trait
bonus is halved once more meaning it isn’t that much at all.
We naturally have an auto assign option for leaders that will take some
of the headache out of managing the whole command structure, but you
may want to guide the careers of those generals you favour. Also to
help here each commander in combat gains experience. So corps of 3
divisions attacking will see all 4 commanders gain experience.
On to Divisions themselves. Since we last talked about them we have
been working away testing and refining the system. This allows us to
give more definitive answers about how the division system works. First
up we can confirm the existence of the single brigade division (which
if you use counters will be marked with a single x to denote it’s
brigade status). This formation has a distinct disadvantage over other
divisions in that it cannot have a commander, meaning it won’t receive
any bonuses in combat. Secondly brigades can be transferred to and from
divisions. You decide if you want to increase the number of your tank
divisions by stripping out a tank brigade and replacing with a
motorised, then feel free to. Similarly want to replace cavalry with
armour? You can simply build an armoured brigade, add it to the
division and remove the cavalry brigade. Then you either disband the
cavalry or do something else with it.
#######################################
# Each trait can have ONE effect of the following
#
# xp_gain surprise_chance supply_consumption defence_modifier offence_modifier combat_move_speed winter_attrition river_attack
# fort_attack combined_arms_bonus out_of_supply_modifier submarine_attack disengage_timer spread_out spotting_chance defender_softness
# strategic_attack naval_attack night_attack tactical_attack dissent_impact encirclement_bonus envelopment_bonus experience_bonus
# fort_defence amph_attack digin_bonus paradrop_mission
#######################################
##################################
# Common Traits
##################################
old_guard = {
xp_gain = -0.5
}
trickster = {
surprise_chance = 0.1
}
##################################
# Land traits.
##################################
logistics_wizard = {
supply_consumption = -0.25
}

And for you modders out there... Here is how traits are defined, and of course, you can add as many traits as you want..