It's the loyalty required for the officer to stay loyal to you.
On a scale of 1-20
1 makes him an extremely loyal person who never betray.
20 means he is very hard to please and would require multiple bribes and possibly a marriage.
You can see the loyalty modifiers and how they work in game here...
Another interesting aspect is the more loyal that officer is, the more he's giving all he's got when tasked.
Out of the four statistics, Politics is the dump stat for combat.
Leadership, Valor, Intellect actually matters in battle. An officer like Lu Bu would prevail easily when he meets anyone in open battle. But if he meets someone with high intellect that enemy may trigger a Night Attack upon commencing battle. He is literally screwed since he starts the battle with his entire army paralyzed for a short time. Not to mention possessing low intellect makes him vulnerable to Obstruction tactics that tend to slow, paralyze, or even confuse his men into attacking other friendly targets. Similar to RTK11 you can attach up to 2 adjutants to cover such weakness and bolster the unit with additional unique tactic option.
In my game I attach Yuri with my daughter Sakae.
Yuri has the Heavy Crush tactic that ignores terrain penalty when rushing and increases attack greatly for a moderate amount of time. Sakae has Swift tactic, that increases movement speed in battle. Activate both tactics for 3 Bars of Control, and end it with a Cavalry Charge costing 2 Bars for maximum effect. Even a slight numerical disadvantage is meaningless, his charge would result in a rout for the enemy most of the time.