In “Less than Nothing,” Slavoj Zizek provides the best explanation of Hegelian Reconciliation (the Hegelian Triad!) I’ve ever read:

This is how Hegelian reconciliation works—not as a positive gesture of resolving or overcoming the conflict, but as a retroactive insight into how there never really was a serious conflict, how the two opponents were always on the same side (a little bit like the reconciliation between Figaro and Marcellina in The Marriage of Figaro, where they are brought together by the realization that they are mother and son). This retroactivity accounts also for the specific temporality of reconciliation. Recall the paradox of the process of apologizing: if I hurt someone by making an unkind remark, the proper thing for me to do is to offer a sincere apology, and the proper thing for her to do is to say something like, “Thanks, I appreciate it, but I wasn’t offended, I knew you didn’t mean it, so you really owe me no apology!” The point, of course, is that despite this final result, one still has to go through the entire process of offering the apology: “you owe me no apology” can only be said after I have offered an apology, so that although, formally, “nothing happens,” and the offer of apology is proclaimed unnecessary, something is gained at the end of the process (perhaps, even, a friendship is saved).

Later, in a footnote, Zizek adds:

A scene in Ernst Lubitsch’s wonderful To Be or Not to Be, a short dialogue between the two famous Polish theater actors, Maria Tura and her self-centered husband Josef, playfully subverts this logic. Josef tells his wife: “I gave orders that, in the posters announcing the new play we are starring in, your name will be at the top, ahead on mine—you deserve it, darling!” She kindly replies: “Thanks, but you really didn’t have to do it, it was not necessary!” His answer is, of course: “I knew you would say that, so I already canceled the order and put my name back on top …”

He also adds an example from the Christian religion:

In short, (for Hegel) the ultimate deception lies in the failure to see that one already has what one is looking for—like Christ’s disciples awaiting his “real” reincarnation, blind to the fact that their collective already was the Holy Spirit, the return of the living Christ. Lebrun is thus justified in noting that the final reversal of the dialectical process, as we have seen, far from involving the magical intervention of a deus ex machina, is a purely formal turnaround, a shift in perspective: the only thing that changes in the final reconciliation is the subject’s standpoint—the subject endorses the loss, re-inscribes it as its triumph. Reconciliation is thus simultaneously both less and more than the standard idea of overcoming an antagonism: less, because nothing “really changes”; more, because the subject of the process is deprived of its very (particular) substance.

Generally speaking, reconciliation works through the addition of a superfluous element, one that only becomes superfluous a posteriori, once you already added it:

Here also, then, one has to do something (offer an apology, enact a reign of Terror) in order to see how it is superfluous. This paradox is sustained by the distinction between the “constative” and the “performative” dimensions of speech, between the “subject of the enunciated” and the “subject of the enunciation”: at the level of the enunciated content, the whole operation is meaningless (why do it—offer an apology, go through the Terror—when it is superfluous?); however, what this common-sense insight forgets is that only the “wrong” superfluous gesture creates the subjective conditions which make it possible for the subject to really see why the gesture is superfluous.