Narcissa Malfoy flees in the dead of night to Snape's house, with Bellatrix Lestrange hot on her heels.
Narcissa seeks Snape's help and counsel, but Bellatrix tries to stop her, knowing that she would be going against Voldemort's orders to do so.
Snape accepts the two women into his house and orders Wormtail (who Voldemort has sent to Snape as a servant of sorts) to bring some wine.
Narcissa wants to tell Snape that Voldemort has ordered Draco to engage upon a dangerous quest, but Bellatrix doesn't trust Snape and tries to keep Narcissa from spilling the beans.
As it so happens, Snape already knows about Draco's mission.
Narcissa wants Snape to talk to Voldemort and get him to change his mind. Completely beside herself with worry for her son, she cries, "Why, Severus? Why my son? It is too dangerous! This is vengeance for Lucius's mistake, I know it!" (2.129).
(Refresher: In Book 5, Lucius led a failed attempt to steal the prophecy about Harry Potter from the Ministry of Magic. He got caught and is now in Azkaban.)
Bellatrix and Snape try to tell Narcissa she should be proud that Voldemort has given her son such an important duty.
Narcissa asks Snape to make an Unbreakable Vow to protect her son. She makes Snape swear to carry out any task should Draco not be able to do so.
Much to Bellatrix's surprise, Snape agrees to all of this.