Eyeball orders, otherwise known as 'eyeball-to-eyeball orders' in military parlance, are those that have been given directly by the commander to the individual being ordered (e.g. while they're looking directly at you to ensure that understanding has occurred), with the implication that there's no scope for creative misinterpretation.
For example, instead of saying "Defend along this line,” I prefer to
elaborate with, "Do not allow the enemy to get south of this line with
anything larger than a com- pany, and do not allow direct fire on this
road. You may give ground to the south of this mountain temporarily,
but you must eject any force that gets there.” The two missions that
require the most lengthy explanations are "delay” and "screen.” Those
jobs are very hard to do under the best of circumstances, and they
become impossible if the doer does not grasp what is demanded of him.
Along with a careful description of what is desired, there should be
an explanation of why. Only through an awareness of what the boss
is trying to accomplish can subordinates make intelligent decisions that will support the purpose.
Eyeball-to-eyeball orders provide a chance to sense if intentions are fully
understood. Accomplishing this well forward in the area of operation also gives
an opportunity for commanders to see the ground together and to share views and
firsthand knowledge. That becomes especially important in the attack.
Quarterly Review of Military Literature, Volume 62, Issue 7