The Woman in Black is one long trip down memory lane, but it's not the memory lane that happens to be lined with rose bushes and chirping birds and lazy afternoons at the beach. It's more a memory lane that's lined with boggy marshes and skeletons. Not so pleasant. The whole tale of the woman in black is one that will live forever in Arthur's memory, for better or for worse (hint: it's totally for worse).
The woman in black could represent anyone who is so stuck in the past that he or she can't move on with life.
No matter how much Arthur tries to leave the past behind—both in the sense of his personal past and a historical past—it always catches up to him.