The turning point, the crucial period; the defining moment.
When Sparrow isn't traveling through time to find his next story, he can often be found in the present day, experiencing a new twist on relatively contemporary issues.
These stories take place in a time very much like our own, and in a world very much like our own. In fact, the audience could be forgiven for believing that these stories are actually happening, or have just recently happened, or will soon happen.
The storyteller probably believes the same.