Doppelgangers
Doppelgangers, also known as Shadow Selves, are a supernatural occurrence that was created by nature after Amara and Silas became true immortals. It was a way to maintain the balance in nature. Doppelgangers were "fated" to be together, with each new set of doppelgangers the supernatural world would "work" to push these two doppelgangers together, for example, Stefan and Elena are both doppelgangers and were portrayed to be drawn together. One of the most important things about doppelgangers is their blood, it is special to travels and is the key ingredient for a lot of the big spells.
Amara
Amara was the start of doppelgangers. She was the first girl doppelganger and when she became immortal, she started the line of doppelgangers.
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Silas
Silas was also the start of doppelgangers. He loved Amara so much that he wanted to love her for eternity, so he convinced Qetsiyah to make the immortality spell and him and Amara took it. This upset the balance in nature and that's how Silas became the first male doppelganger.
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Elena Gilbert
The whole reason Stefan was drawn to Elena was because of her resemblance to Katherine Pierce. When Stefan found Elena, he had no idea what she was or who she was. Once Elena and Stefan started dating that's when they looked into the resemblance and discovered that Elena was a doppelganger.
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Stefan Salvatore
Stefan doesn't discover that he is a doppelganger until he met Qetsiyah, and she told him about Silas and the story of Qetsiyah and Silas. The main supernatural characters that found doppelgangers important are Klaus, Qetsiyah, and the travelers.
Katherine Pierce (Katerina Petrova)
Katherine is the descendent of Amara which means that Elena descended from Katherine. Katherine was always jealous of Elena, and she was portrayed as the complete opposite of Elena in every aspect. She is also a survivor, but she has many enemies.
Tom Avery
Tom Avery isn't really involved in the vampire diaries at all. He is in one episode, and it is because the travelers want him dead so that Stefan is the only remaining doppelganger left for the guys. They needed Stefan to be the only doppelganger left so they could bring their leader back to the land of the living, they did this by doing a specific spell involving Stefan and Elenas blood.