"Will you, Severus, watch over my son, Draco, as he attempts to fulfill the Dark Lord's wishes?"
-- Narcissa Malfoy (HBP2)
Snape and Narcissa take the vow together, with Bellatrix serving as Bonder. Snape agrees to help Draco with his task and to finish it for him if Draco fails (HBP2).
You have to love this exchange, from HBP16:
"Yes, Snape was offering to help him!" said Harry. "He said he'd promised Malfoy's mother to protect him, that he'd made an Unbreakable Oath or something —"
"An Unbreakable Vow?" said Ron, looking stunned. "Nah, he can't have. . . . Are you sure?"
"Yes, I'm sure," said Harry. "Why, what does it mean?"
“Well, you can't break an Unbreakable Vow. . . ."
"I'd worked that much out for myself, funnily enough. What happens if you break it, then?"
"You die," said Ron simply. "Fred and George tried to get me to make one when I was about five. I nearly did too, I was holding hands with Fred and everything when Dad found us. He went mental," said Ron, with a reminiscent gleam in his eyes. "Only time I've ever seen Dad as angry as Mum, Fred reckons his left buttock has never been the same since."
"Yeah, well, passing over Fred's left buttock —"
"I beg your pardon?" said Fred's voice as the twins entered the kitchen.
But one has to appreciate the odd position Snape has now placed himself. He has promised to kill Dumbledore twice: once to Dumbledore himself and now to Narcissa. And doing so will force him to give up the carefully crafted position in the eyes of both sides of this conflict. Snape must have spent much of this following nine months working to create his plans to escape when the inevitable happened.