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"Second Advent" refers to the discovery of Earth (Laterre) by the Daban Urnud:

“What happened in the Second Advent—on Laterre?” asked Suur Moyra.

“I will skip the details. It was not as bad as Tro. But in every cosmos they visit, there is upheaval. The Advent lasts anywhere from twenty to a couple of hundred years. With or without your cooperation, the Daban Urnud will be rebuilt completely. None of your political institutions, none of your religions, will survive in their current form. Wars will be fought. Some of your people will be aboard the new version of the ship when it finally moves on to some other Narrative.”

“As you were, I take it, when it left Laterre?” asked Lodoghir.

“Oh, no. That was my great-grandfather,” said the visitor. “My ancestors lived through the voyage to Fthos and the Third Advent. I was born on Fthos. Similar things will probably happen here.”

A trailer for the fictional television series based on these events can be found here: