The command tree is easy to leave on autopilot, but a general with the right traits can change the outcome of an even battle. Here's the essential part, so you don't ignore it entirely.
Generals and Field Marshals
A general commands an army (a group of divisions assigned directly to him). A field marshal is a level above: he oversees several generals and their armies within an army group, contributing his own bonuses to the whole. You don't need field marshals in small games, but in wars with many simultaneous fronts they organize command far better than leaving each general on his own.
Command Traits
Generals gain traits from combat experience, or can be trained beforehand if you have officer academies or focuses that allow it. Some traits are general-purpose (improve organization or speed), while others specialize in a specific terrain or doctrine. A general with armor traits leading a tank force performs noticeably better than a generic one.
Command Capacity
Every general and field marshal has a limit on how many divisions they can lead effectively without penalty. Going over that limit reduces the performance of the excess divisions. Splitting the army well among several commands, instead of stacking everything under a single general, avoids that silent penalty many people don't even notice they're suffering.
Common Mistakes
The most common mistake is ignoring command capacity and stacking too many divisions under one general, losing efficiency without realizing it. The second is not promoting new generals in time before a big war, entering the conflict with fewer commanders than the army actually needs.