La tua cantante is the Italian expression for a human whose blood particularly appeals to a certain vampire in an extreme sense. In English, it means "your singer", but is usually shortened to "singer" whenever someone refers to her/him.
The smell of each human is different, and certain humans smell more appetizing than is usual to vampires. The more appealing any human's scent and taste is to a vampire, the more difficult it will be for that vampire to leave the human alive.
Infrequently, a specific human will smell nearly irresistible to a specific vampire. "Singers" are individual phenomena; a person whose blood sings for one specific vampire will not have the same effect on all vampires, though they may still find the human mouthwatering (As Laurent said to Bella when she was in the meadow where she and Edward used to hang out before he left Forks). While there are some humans whose scents are more appealing to vampires in general, that appeal does not reach the level of a singer.
Singers are considered by most vampires to be a great find, the drinking of whose blood is an experience to be savored.
Bella was Edward's singer prior to her becoming a vampire. He was so appealed by her scent that he found his throat burning and ached to drain her blood, and barely retained enough self-control keep from killing her. The blood of singers is described by Edward as being said vampire's "own personal brand of heroin". Eventually, his restraint developed to the point where her blood no longer bothered him, and he personally changed her into a vampire.
Emmett had stumbled upon two singers, one tasted better than the other. Neither was left alive because he lost control the moment he smelled their blood.
Alice was James's singer before she became a vampire. James stumbled across her old, faint scent in Biloxi in 1920 and tracked her down. Alice realized her doom the moment James caught her scent and her creator turned her into a vampire to save her. When Alice was turned, James was furious that he never had a chance to taste her blood and killed her creator.