Watching this, Dumbledore says something like:
"... but you must wait until Voldemort is at his most Vulnerable.."
Dumbledore asks that Snape reveals Harry Potter where Snape's true allegiance lies, and also that Harry must die in order to kill Voldemort.
I think this is a reference to Voldemort's horcruxes - when they are destroyed. As far as I can remember, Dumbledore never told Snape about the horcruxes . Even so, I think they had a quarrel about Dumbledore not sharing all the details with Snape.
So, how did Snape figure out when Voldemort was at his most vulnerable?