Enhanced self-preservation is Victoria's power to sense and escape any danger.
With this power, Victoria could identify any sort of danger coming at her the moment the ill will is directed, as demonstrated when she sensed James hunting her before they became a couple. Another example is when the Volturi came to recruit Heidi, and Victoria sensed that the Volturi were going to kill her and her coven mates after acquiring Heidi's talents.
It also allowed her to instinctively know how to evade an attack and know whne to run without any particular planning ahead. For instance, when Jasper and Emmett made their moves on her, she easily dodged their pursue by inches and jumped into the Quileutes' territorial lands, sensing that they wouldn't cross over.
Bella Swan noticed her ability because while she was fighting Edward in Eclipse, her feet seemed to bring her to a safe place while warring with her lust for revenge. It is described as the feeling of being pulled to safety.
Because of this power, she was a very difficult opponent to be defeated by the Cullens. Whenever she found herself facing danger, her instincts were to run.
This power only worked on the user alone. Whenever Victoria was in danger, she would feel compelled to run away, and any desire to stay would become secondary as her desire to survive was too great for her to suppress, unless she was angered to a level strong enough to war with that instinct. It is very likely that her ability to detect danger is limited only to those coming from her enemies with the intent to kill.
While holding Harry Clearwater in the New Moon movie, Victoria seemed unaware of Jacob's presence when he tackled her to save Harry. This implied that she could be unaware of danger if her mind was occupied or it was simply because Jacob was focused on saving Harry instead of attacking Victoria.
This power is rooted in her ability to escape pursuers when she was human, being able to hide or run away without getting caught. She worked as a housemaid for most of her life, but lived rather poorly because of her abusive masters; subsequently, she learned to hide from them, and that skill improved over the years after her sister mysteriously disappeared. Using this skill for survival, she managed to live on the streets for two years; she snuck into the smallest places of houses to sleep and stole as little food as possible to avoid notice. She could also avoid notice of animals.
As a vampire, her survival skill become uncanny, allowing her to sense and evade danger. When the Volturi came to destroy her coven, she was the only one who survived (other than Heidi, who was claimed by the Volturi), and had avoided contact with all vampires since then. While being chased by James, she managed to escape him for months until he became interested in her talent. When his ill-will toward her faded, so did her urge to escape, which allowed him to catch up to her.
Being with James, she learned to take bigger risks and use her power to her advantage.
In Twilight, when Victoria's mate, James, died at the hands of the Cullens, she escaped their pursuit with her power as her compass and created a newborn guard for protection in Seattle. Laurent warned the Cullens not to underestimate her while they made it their mission to kill James.
While being pursued by Edward Cullen in New Moon, she sensed the danger and shook him off in Texas, where she encountered a small coven of newborn vampires and evaded them as well.
When she returned to Forks in an attempt to make an easy move on Bella, she was caught off-guard by the Uley pack. Though she managed to avoid their assault, she continued to make attempts to get past them and failing; with her powerful survival instinct, it was difficult for her to make a bold move on Bella, though it did save her from being killed by the wolves. On one occasion, Victoria escaped into the ocean while being chased by the pack.
The hunt was seen in the movie where she manages to evade Jacob Black's attack and then escape the wolves by jumping into the ocean. None of the other wolves managed to come close to catch her, except Jacob. On one occasion, Jacob manages to knock Victoria away before she notices him; though he was most likely doing so to protect Harry Clearwater and so her power failed to detect danger.
In Eclipse, Emmett attempted to jump on Victoria while the Cullens and the Uley pack were chasing her across the woods, only for her to sense his assault and evade him, and as a result land right into shape-shifter Paul, and almost started a fight. Victoria used this as an opportunity to escape.
In the movie, she was being hunted by the Cullens and the Uley pack, but managed to avoid capture and then escape through the Quileute tribal lands; Emmett touches her should while chasing her, but she throws him off. When Jasper tries to catch her in the air, she flips her body to avoid him. Then, as the wolves are coming close to catching her, she runs to the side to avoid their attacks and jumps across the ravine.
While in the clearing with Bella, Edward, and Seth, Victoria took Riley with her as a device to distract Edward long enough for her to kill Bella. When Seth fought with Riley, she tried to escape. However, Edward, finally noting her ability, frequently taunted her relationship with James in order to put a stop to her threat - permanently. After successfully angering her, a battle erupted between them. The two were on par with each other due to Victoria's ability of evasion and Edward's ability to read minds.
When Riley died, Victoria realied her disadvantage and tried to escape, but Edward anticipated her mind and caught her before she could sense his coming, and subsequently killed her with his own hands.