"Severus, will you swear it? Will you make the Unbreakable Vow?"
-- Narcissa Malfoy (HBP2)
The Unbreakable Vow creates a magically binding vow between two people. The spell apparently cannot be performed using wandless magic (judging from Snape’s remarks to Bellatrix rather than from the Weasley twins’ underage efforts) and requires that the Bonder’s wand be touching the joined hands of the person administering the vow and the person taking the vow. As each clause of the oath being sworn is agreed to, a thin tongue of brilliant red flame shoots from the caster’s wand and winds itself around the joined hands of the participants, remaining in place as other clauses of the oath are sworn to.
If the person breaks the vow to the other person, they will die – there is no “out” clause in the Unbreakable Vow contract.
References from the canon
Snape agreed to three things during the Unbreakable Vow. First, he would watch over Draco as he does the Dark Lord's bidding. Second, he would try to protect him from harm. And third, if Draco failed in his task, Snape had to complete it.
The first two were easy answers, since Snape was a teacher at Hogwarts and Head of Slytherin. It was his job to watch over Draco, just as he watched over everyone else. The third part was more difficult, and it's unclear whether Snape actually knew what Draco was supposed to do for the Dark Lord.
But by then, Snape knew that Dumbledore only had a year to live, and that he himself only had a year to teach Defense Against the Dark Arts thanks to Voldemort's curse on the position. The only thing that put Snape in real jeopardy was the duel between Harry and Draco in the bathroom during which the Sectumsempra curse nearly killed Draco. If he had died, then the Vow would have killed Snape too. Luckily, Snape knew the counter-curse and was able to save Draco's life.