The device is 'personification', which is a form of metaphor. What personification does is to give human qualities or attributes to something that isn't strictly a human. So here, the abstract noun 'death' is turned into a metaphorical person, capable of doing things: and given, you'll notice, a capital letter to denote a proper name.
'Death', then can perform human actions: he can be Capulet's son-in-law and heir, he can marry Juliet, and when Capulet dies (this is the end of your quote!) he will leave all his money to this Death. Is he being literal? No. He's pointing out despairingly that, instead of his daughter being married to Paris, as he had hoped, she has become married, metaphorically to Death: she has died.
Incidentally, to aid your understanding of this quote (and, actually, this play) it might be worth my pointing out that 'death' to the Elizabethans meant 'orgasm' as well as the noun from the verb 'to die'. So death and sex are always related in this play, which, if you think about it, gives a whole new spin to 'Romeo and Juliet''s odd combination of passion and love with violence and hate.
Hope it helps!