"But she'd (Elena) always heard that the souls of true lovers were connected somehow...by a silver string from heart to heart or a red cord from pinky to pinky. To her delight, she found it almost immediately. A thin cord the color of moonlight, that seemed to be stretched taut between the sleeping Elena's heart, and...yes. When she touched the cord, it resonated so clearly to her of Stefan that she knew it would take her to him."
Soulmates are the concept that each person has a person with whom they belong to. It manifests as a silver cord connecting two hearts and is seen between Elena Gilbert and Stefan Salvatore in The Return: Shadow Souls, when Elena utilized it to have an out-of-body-experience to contact Stefan.