It's an important plot dump, explaining that they changed history.
When they sabotaged Cedric as Durmstrang boys, Hermione suspected Durmstrang was behind it.
So she refused to go to the ball with Viktor Krum.
That led to Ron never getting jealous, which meant they never fell in love.
Albus thinks they need to go back in time—again—to fix things.
Scorpius tells Albus to get over his daddy issues, because they're making him a terrible friend.
Professor McGonagall, using the Marauder's Map, almost finds the boys, but they hide under Albus' invisibility cloak.
After the scare of almost being found, Albus admits to Scorpius that he doesn't believe he's Voldemort's son because he doesn't think, "Voldemort is capable of having a kind son" (2.16.78).
That's enough to make them friends again.
With Albus and Scorpius' friendship re-cemented, they agree to find their way back to the Triwizard Tournament.