In a fight, you can maneuver better. It causes drag situations, as the automatic-ness is constantly maintaining what it is trying to achieve when set on.
Turned off, then, you will need to manually trim it out, which changes due to altitude, speed, etc.
I have my Combat Trim as a button mapped as an on/off toggle.
There is write-up somewhere in the training section, and probably in the wiki.
I think CT is Aces High way of dealing with a PC simulation's characteristics mimicing real life.
I usually have it on, but then as needed.
I remember a guy wrote up a sortie taking out his P-47 and how he used combat trim as needed and why.
Do a search here to AH Forums.