St. Thomas considers human happiness to be both an end toward which men strive, indeed the last end upon attaining which there is no other unsatisfied desire present; but also an act or simply activity.
Thus, when asked, "What makes you happy?" one might answer, "eating pie" or "playing soccer." Eating pie in the present and immediate future will then be the essence of happiness.
Our author of course considers the perfect happiness-generating activity to be "seeing God." Hence he says that the beatific vision as an act of the intellect is the essence of happiness. Doing what you enjoy is the definition of happiness.
The pleasure or joy in that activity, of contemplating God, is an act of the will which is not the essence of happiness but "its proper accident."
I actually don't like this analysis. For example, it seems that seeing God is not the essence of perfect happiness but its cause. Regarding human action, we have the <desire, plan, execution> trinity corresponding to <will, intellect, power>: I first perceive a desire to attain some end, then form a plan of using various means, and finally put the plan into motion.
Regarding human enjoyment, we have the <fruition, vision, comprehension> trinity: this time in the reverse order, I first own or possess or grasp a good, then use it for my own benefit intelligently, and finally enjoy its services and rest therein.
In that case it's the entire enjoyment trinity that constitutes happiness. As St. Thomas himself argues, "good results from the entire cause, evil from each particular defect." He reckons similarly:
For even among ourselves not everything seen is held or possessed, forasmuch as things either appear sometimes afar off, or they are not in our power of attainment.
Neither, again, do we always enjoy what we possess; either because we find no pleasure in them, or because such things are not the ultimate end of our desire, so as to satisfy and quell it.
But the blessed possess these three things in God; because they see Him, and in seeing Him, possess Him as present, having the power to see Him always; and possessing Him, they enjoy Him as the ultimate fulfillment of desire. (ST, I, 12, 7, reply 1)
We may then rephrase the matter as follows:
Comprehension as an act of power is the "prior" condition of happiness, i.e., the ability to squeeze utility from God securely. You own your reward in heaven.
Vision as an act of the intellect is the "immediate" source of happiness: the activity of seeing God now and forever.
Fruition as an act of the will is the "posterior" consummation of happiness, or the peace and joy of union with God.
All three together make up indeed the essence of happiness.