When people recognise that past actions affect present situations.
Like the Archbishop of Canterbury recognising the role that organisation played in keeping slaves even after the abolition of slavery.
It is hard to imagine the theological loopholes that must have been jumped through to justify such ownership, or miss the breathtaking irony that the money those slaves generated was used to pay for missionary work. Talk of reparation in terms of hard cash also sounds similarly like opportunism to me - the same attitude to making money from the efforts of forbears as the slavers had.
It seems to me that, just as we remember war as the terrible thing it is, so we should remember slavery in the same manner. My one fear with this: that it will be treated as lightly - something to be adopted in the future as we perceive needs must.