Micro'ing your Capitals just means you take the time to position them individually and select their targets and abilities manually.
For example, most Capitals do not have all their weaponry mounted on the front, it is scattered around all sides. So in some battles, you would want to manage your Capital to keep it in the middle of an enemy group (particularly militias) so it can use as much as it's weaponry as possible.
Special abilities of many ships also requires a good deal of micromanagement at times. Some abilities can be left on autocast and the AI will handle it fine (Gauss Cannon on the Kol comes to mind) but other abilities, particularly Level 6 abilities you simply have to manage yourself if you want them to have the best effect. You wouldn't want an Akkan with Armistice on autocast and completely halting a battle that you're winning, but keeping that ship ready and easily accessible so that you can deploy this ability when it's most advantageous to you.
You have a lot to benefit though from micromanaging your Capitals, as well as other ships with active abilities. But more importantly, the AI for the autocasting can be weird or very ineffective (having multiple ships use the same ability on the same target, using a powerful ability on a ship about to die, etc.) so keeping the ones you feel comfortable managing yourself not on autocast can save you a great deal of grief.
