Sorceress' Knight
The term 'Sorceress' Knight' refers to the guardian of a sorceress - someone whose role is to protect her from outside threats and, perhaps just as importantly, from the dangers that come with her own power. There is something almost romantic about the idea, with the knight completely devoted to the sorceress he has sworn to protect.
For Seifer, becoming a Sorceress' Knight is much more than simply taking on a role. It has been his dream since childhood, and he seems to have built an entire idea of heroism and greatness around it. When he finally becomes Edea's knight, it feels like he has stepped into the story he has always imagined for himself. Even after everything begins to fall apart, he continues to hold onto that identity.
The idea of a Sorceress' Knight also exists beyond Seifer. At the orphanage, Edea refers to Cid as her knight, suggesting that the role has a history that goes back further than Seifer's own story. It gives the title a more personal meaning as well, rather than making it simply another position within the world of SeeD.
For Seifer, though, the romantic image of the Sorceress' Knight is clearly what matters most. He doesn't seem interested in the role simply because it gives him power. He wants the glory, the purpose, and the feeling of being someone important. In his mind, becoming a Sorceress' Knight means finally becoming the hero he has always wanted to be.
Origin
According to the Final Fantasy VIII Ultimania, a famous film exists within the game's world about a sorceress defending her land with the help of her knight. The movie is strongly implied to be the same film starring Laguna Loire as the knight - something we actually get to see during one of Laguna's flashbacks.The game never outright says that this movie is what inspired Seifer's dream, but the connection is hard to miss. Seifer seems to have grown up fascinated by the romantic image of the Sorceress' Knight presented in the film. He even imitates the actor's Gunblade stance and fighting style, which makes the influence feel pretty deliberate.
And there is something rather bittersweet about that. Seifer dreams of becoming the heroic knight from the stories - someone strong, admired, and devoted to his sorceress. When he finally gets the chance to become one, however, reality looks very different from the fantasy he grew up with.
Instead of becoming the gallant hero he imagined, Seifer ends up caught in someone else's plans. He believes that he has finally found his destiny and that he is the one in control, while in reality he is being manipulated by Ultimecia. The dream he spent so long chasing does come true in a sense - just not in the way he ever imagined it would.
Loss
Even after everything falls apart and he is ultimately left behind, Seifer still holds on to the identity of the Sorceress' Knight. It's almost as though he can't quite let go of the dream that gave him so much purpose in the first place. For so long, becoming a knight was the future he imagined for himself, and giving that up would mean admitting that the dream he chased so desperately didn't turn out the way he had hoped.Seifer's story isn't really a traditional hero's journey. It's the story of someone who had a very specific idea of what being a hero meant and pursued it with everything he had, only to discover that reality doesn't always resemble the stories we grow up believing in. Whether Seifer ever fully understands how far he has strayed from his original dream is left open, but the contrast between the knight he imagined himself becoming and the man he eventually becomes is one of the most interesting parts of his character.