Rukia Kuchiki was the first character to ever appear in Bleach and, fittingly, she's the most important, too. At first, Rukia's resume and personal history wouldn't suggest her enormous importance. She and her big sister Hisana grew up poor and desperate in the Rukongai district, and Rukia suffered another loss when Hisana abandoned her. Still, Rukia managed to make it as a rank-and-file Soul Reaper, and she was a credit to the uniform. Then, she hunted a Hollow named Fishbone D in Karakura Town, and that was when everything changed.
What Rukia did not know is that she was a major cog in the treacherous Sosuke Aizen's evil plan. At an unknown point in the story, Kisuke Urahara used Rukia's body as the hiding place for his monstrous invention, the Hogyoku, and planned to keep her out of Aizen's grasp. Rukia ended up living in a gigai (false body) for weeks on end, and Kisuke designed it to leech out Rukia's spirit energy. Thus, she'd eventually end up as a regular human girl, and become nearly impossible for Aizen to find. But he was too late.
Aizen was privy to Kisuke's plan, and he arranged for Rukia to visit Karakura Town and illegally give her powers to a certain Ichigo Kurosaki. Doing so would give the Soul Society a reason to arrest her and then execute her via a flaming weapon, destroying her body and revealing the Hogyoku inside.
Ichigo Kurosaki already had enormous spiritual potential through both his mother and father, but his first taste of power came from Rukia when she crossed his path that fateful night. Ichigo was sure that he was an ordinary adolescent, aside from his ability to see ghosts, but Rukia took things to the next level. After an awkward first meeting, Rukia explained her job and the Hollow she was hunting, and Ichigo followed her onto the battlefield. Fishbone D, a large Hollow, had captured Ichigo's sister Karin and tried to devour her, until Rukia attacked. She was injured, and Ichigo was left as the only option to save Karin's life.
So, Rukia thrust her zanpakuto into Ichigo's chest, transferring her power to him. This gave Ichigo his first (nameless) zanpakuto, and he used it to slay Fishbone D in just a few strikes. Ichigo would undergo some more training after that, and once this nameless zanpakuto broke, Ichigo trained again with Kisuke Urahara to unlock Zangetsu. But he couldn't have gotten that far without Rukia's help in the first place.
Rukia wasn't totally alone before she met Ichigo, however. Captain Byakuya Kuchiki, the head of the Kuchiki noble family and commander of Squad 6, had already formally adopted her into the family. Hence, Rukia Kuchiki. Byakuya had broken the rules by adopting Hisana into the family, however, and he resolved to never break a rule again for any reason. He also had a polite but distant relationship with Rukia, his sister-in-law, and he had a similar relationship with his Lieutenant, Renji. However, Renji was closer to Rukia, since they had grown up in the same impoverished town before their Soul Reaper days. Rukia was a good friend to Renji, but duty came first. Then, Rukia was charged with the crime of giving Ichigo her powers.
Byakuya followed the letter of the law and defended Rukia's sentence, whatever his personal feelings. Renji did the same, and fought Ichigo over Rukia's fate. At first, Renji was determined to uphold his Captain's view, but after losing to Ichigo and seeing his passion for rescuing Rukia, Renji had a change of heart, and practically begged Ichigo to rescue his dear friend. Thus, Rukia became the catalyst for Ichigo's and Renji's fruitful friendship and alliance.
A similar story played out when Ichigo had his climactic battle with Byakuya at Sokyokyu Hill, the site of Rukia's planned execution. Ichigo struggled against Byakuya, but managed to fight him to a draw, and Byakuya began to see things Ichigo's way. Or at least, become more sympathetic. Soon, Aizen and his followers, Gin and Kaname, arrived and extracted the Hogyoku, outing themselves as traitors. Byakuya, inspired by Ichigo's defense of Rukia, took a blow for Rukia's sake. Like Renji before him, Byakuya urged Ichigo to protect Rukia at all costs. This newfound alliance would continue into the next story arc, when Byakuya gave Rukia and Renji his blessing to sneak off to Hueco Mundo to aid Ichigo.
Rukia thought she was an unremarkable Soul Reaper. But she was the key to Aizen's plan, gave Ichigo his first step into the spiritual world and transformed Byakuya's and Renji's way of thinking for good.