The Cinderella Story
Kubo doesn't give us much by ways of romance in the series, and in fact keeps most relationships intentionally ambiguous. Byakuya and Hisana's story--or the little we know of it--fills this void with the strength of its devotion and undisputed love.
Worlds Apart
They said it would sully our reputation.
Hisana was the elder of two sisters born into one of the poorest areas of Soul Society. Her ill health and lack of faculties put her so deep into the red that she had to abandon a baby Rukia and try to fend for herself. That loss haunted her for the rest of her life, and she never forgave her weakness.
How such a woman even had the chance to meet Byakuya, the very pinnacle of aristocracy, is a popular mystery to dwell on. Did his duties as a shinigami bring him to the commoners' sector where their paths crossed? Was it love at first sight? Perhaps he saved her from the edge of death on a whim, then developed feelings later? Did Byakuya actually do any flirting, or was it a quieter, more devotional affection from the start?
No matter how you spin it, it's all just as magical. Byakuya could have had his pick from any blue-blooded girl in Soul Society, and yet he presumably fought tooth and nail (he mentions that the union was against family law and tradition) to marry a complete nobody. A prince who didn't throw away his title for his love, but rather made his love a princess--can't get much more romantic than that.
The Tragedy
Hisana's last words say so much about Byakuya, but also ask just as many questions. This confirms that, just as he was willing to break tradition to marry her, he remained completely devoted to her during their time together. He supported her in her search for Rukia, which spanned almost every day, and bore her emotional burdens. If he had married a noble, would he have had to suffer this much? It would be very unlikely, and I'm sure he took that into consideration. Only love could have persuaded such a man to choose the more perilous road, and the suffering was grave indeed.
I'm sorry I cannot... repay the love you gave me... The five years I spent with you were like a beautiful dream...Byakuya-sama...
As I already alluded to in nobility analysis, no one seems to be able or willing to comment on any change in Byakuya's demeanor in the past century. By the time he meets Rukia, a year after Hisana's death (40 - 50 years prior to the start of the series), he is already the hardened man fans know him to be. Was her death the catalyst for his ice cold temperament, or did he show only Hisana his softer side and his mask to others? The question is still unanswered, but at least Rukia guides him back to the light.