Immortality is the ability of eternal youth and infinite lifespan. It is worth noting that 'immortality' in the world of The Vampire Diaries is not immunity to death; Elijah stated that every creature must have a weakness and that nature would never allow a truly immortal being to exist.
Vampires are immune to natural death, physical aging, diseases, and illnesses.
The only weapons that can weaken and kill a vampire is werewolf venom, which will infect the wound and spread through the bloodstream. After that the vampire will start to hallucinate and throw up his meals. Ultimately the vampire dies, crazy and suspicious for everything. Vervain can also be used to weaken and slow down a vampire.
The only way to kill a vampire is to rip out their heart, burn or decapitate them, and the most well known method, a wooden stake through the heart.
Silas was said to be the world's first immortal creature and the only true immortal.