Throughout the Twilight series and After Breaking Dawn, gifted humans are humans who manifest special abilities or strong qualities before they are turned into vampires. After they are turned, that characteristic will likely magnify into a supernatural talent. Depending on the clarity of its human manifestation, the level of that talent varies after the change.
The Quileute tribal members descended from Taha Aki manifested magical powers that allowed them to transform into giant wolves, though these powers only activate for the fitting age and after coming across a vampire. This and the telepathic link between them in wolf form identifies them as "gifted". However, unlike humans, these people are unable to transform into vampires after getting bit. The venom simply works as poison to their systems.
Bella Swan is capable of shielding her mind from all sorts of psychic powers. As a vampire, she becomes able to extend her shield to protect someone other than herself, effectively keeping all mind-invasive powers at bay. Her power was seemingly inherited from her father.
Charlie Swan manifests a mental defense that reduces the effects of a psychic influence on his mind. This trait was later passed down to his much more powerful daughter Bella. Though he is gifted, he does not become a vampire.
Edward Cullen had been able to read people very accurately as a human. As a vampire, this characteristic evolved into a supernatural ability to read other people's minds, both human and vampire.
Alice Cullen was gifted with a weak but predictable sense of the future. Her predictions weren't always certain and mostly manifested as feelings, but at times she could see them in visions when the future was set. This ability brought to her names and bad reputation as a human. She discovered her father had hired hitmen to kill her mother and later Alice herself through these visions, but was later taken into a mental asylum, where she befriended a vampire. When Alice witnessed her death at the hands of another vampire named James, her friend turned her to save her. After becoming a vampire, her visions were heightened and allowed her to see the future much more clearly, though it still had flaws.
Jasper Hale was very charismatic as a human and he was able to persuade others to think his way. After Maria changed him, his charismatic nature became a supernatural talent that allowed him to feel and influence the feelings of those around him. He mainly used it to keep the wild newborns in the army under control. Whenever he killed someone, human or vampire, he felt their pain.
Lucas Stone can tell something bad is happening or he could suspect what the person feels or thinks and is a skillful martial artist. As a vampire, Lucas can see people’s aura and use his own to block out all sorts of psychic powers as well as shooting aura spheres. His was powers seemingly inherited by his father.
Kendall Stone could detect the feelings of his surroundings and of other people to which he calls them his cop senses. This trait was later passed down to his much more powerful son Lucas. Though he is gifted, he does not become a vampire as he was killed by the Volturi.
Tiffany Stewartheals people with her words whenever they are mentally hurt. She also can understands a person by placing herself in their shoes and see from their point of view. As a vampire, Tiffany can mentally heal scars and injuries and see through a person’s eyes after touching them.
Jalen Long has been able to know the streets at the palm of his hands as well as the people around him which helps him whenever he needs to sneak in to steal food as well as avoiding the cops during his time on the run. As a vampire, Jalen can track a person once he gets the “essence” of a person’s mind on the first encounter. His gift also allows Jalen to detect if his target is coming towards him and help him act before a person reacts.
Jane, and her twin brother Alec, manifested unclear psychic powers to the people around them while they were children. They were able to bring fortune to those who treated them nicely and misfortune to those who treated them otherwise. Aro was told of the twins' latent potential and hoped to change them when they were older. He was forced to change them sooner than expected, when their village accused them of witchcraft and condemned them to burn at the stake. By experiencing the torment of burning death, Jane's anger and desire for others to feel the same pain manifested into an illusionary ability to inflict a burning torment on anyone she saw. After becoming a vampire, Jane's frightening power made her one of the most valuable members of the Volturi guard.
Alec, along with his twin sister Jane, manifested unclear psychic powers when they were children. Anyone who treated him and his family with kindness was often rewarded with fortune while misfortune was brought on those who did the opposite. Aro was told of the twins' latent potential and hoped to change them when they were older. He was forced to change them sooner than expected, when their village accused them of witchcraft and condemned them to burn at the stake. By experiencing the burning pain that nearly killed him, Alec focused fully on escaping the pain and consequently manifested into a power to block senses. After he became a vampire, his paralyzing power made him one of the most valuable members of the Volturi guard.
Niall tends to hide quickly in panic as a human. As a vampire, Niall turns into black smoke whenever he runs very fast. With it, he can avoid being detected by psychic gifts.
James was a skilled and powerful hunter as a human—he was trained to hunt and trap by his father. This skill allowed him to survive by himself when his parents were killed, and later earned him title and fame in the nearby areas. After he was transformed by a French vampire, this skill manifested a powerful sensory that allowed him to detect his prey's movements and track them down.
Victoria led an abusive human life: her employers often assaulted her for any fault or just by being visible. To survive, she learned to sneak and hide from her pursuers, and then survive on her own by stealing food without notice and sleeping in the smallest of corners. After she became a vampire, this surviving skill was turned into a power that allowed her to sense and evade danger. Unlike most gifted vampires, her power wasn't withborn. Rather, her abusive human life had perfected her ability to survive.
Didyme, Marcus's deceased wife, had as a human the dormant ability to induce happiness in others, which prompted her with many suitors. After she changed, it manifested much more strongly. Whoever was with her was always influenced by her happy aura.
Kate was trained to be a bodyguard loyal to whomever she is assigned to protect. As a vampire, her protective instinct allowed her to cause a shock-like jolt in anyone she touches.
Eden Love as painfully shy around others and tends to hide herself as a human. As a vampire, Eden turns into purple haze whenever he runs very fast. With it, she can avoid being detected by psychic gifts.
Sophia Faye was very skilled at avoiding trouble with the police whenever she gets in trouble with the law. As a vampire, Sophia can identify the danger around her.
Benjamin was known to have been an extraordinarily gifted human since he was a child, due to his power to control the natural elements. His distant uncle used his gift for street performance, which prompted Amun to change him. As a human, he only controlled fire, but he began to manifest the other elements after becoming a vampire.
Maggie was born with the ability to sense whether someone was lying. Anyone who tried to tell lies, Maggie pointed them out, which made her a freak to the townsfolk. By becoming a vampire, her gift manifested much more sharply: it allows her to sense others' lies simply by movements and facial expressions that do not come from his or her true intentions.
Alistair was a skilled hunter as a human and enjoyed the company of falcons more than people. By becoming a vampire, his skill turned into a power to feel an elusive gravitational pull to whatever he seeks, even inanimate objects.
Miley Ray is known to torments other people with her insults as well as spreading rumors about them. As a vampire, she is able to shoot mental jabs at someone as well as plant false images in a person’s head and erasing or rearranging their memory.
Max is always a jokester whenever he screws around in class. As a vampire, he can split himself into three clones and run around a person in a triangular motion.
Virgil has always been distant after being used and dumped by the girl he likes. As a vampire, Virgil turns into red smog whenever he runs very fast. With it, he can avoid being detected by psychic gifts.