Mort doesn't have many prospects in his home village, and he really isn't cut out for the family business--he's not nearly serious enough. So at Hogswatch, Mort's father takes him to a hiring fair in the nearby town, where Mort proceeds to wait the whole day while every other person at the fair gets taken in by somebody. It's looking like Mort just won't be hired at all, but right before midnight Death rides up and offers Mort an apprenticeship. Death assures Mort that no, the bones are not required, and Mort accepts the offer.
This is the first of the Discworld novels starring Death, and the fourth book of the series (as far as publication order goes). Lots of fun characters and adventures.