Welcome back to Humor Nation. The main motive of Damon Salvatore was to free his sire and lover Katherine Pierce from the tomb in which she was entrapped. Their relationship goes back to 1864 when Damon who was serving in the army fell in love with Katherine who was staying in the Salvatore Estate. He didn’t know that Katherine was also seeing Stefan, his younger brother. She was using both the brothers to her own selfish motives. However, when Mystic Falls discovered about the existence of the vampires, Katherine was caught and entrapped. The brothers tried saving her, but failed. They died and transformed into vampires due to having Katherine’s blood in their system. Their ship is named as Datherine where as the romantic relationship between Damon & Elena is addressed as Delena.
Damon would eventually confront in Season 2 premiere episode where she first seduces him and then lets him know that she always loved Stefan and never having loved him. This breaks his heart and he ends up snapping Jeremy’s neck to take out his frustration. Even though Katherine had said that she never loved him, but in an exchange with Elena, she reveals that she loved both the brothers.
Although Damon said that Katherine never compelled him which turned out to be false as we saw him getting compelled by Katherine in a flashback scene. There’s an explanation that maybe Damon had a sirebond to Katherine which is why he remained loyal to her throughout the years. But the show creator Julie Plec confirmed that it was true love and not sire bond behind his feelings for Katherine.
It was the search for Katherine which ultimately made Damon cross paths with Elena in Mystic Falls. He compelled her to forget about their first exchange. We only learn about that in Season 3 finale. While Elena at first saw Damon as nothing more than a cruel, evil sociopath who only knew how to use others. However, when she saw the deeper sides of him, she felt attracted towards him. During the time when Stefan was missing, they bonded while searching for him. Elena and Damon both kept denying their feelings until Elena transformed into a vampire and due to sire bond her love for Damon was amplified.