The designation Sword of the Jedi was granted to Jaina Solo by her maternal uncle, Luke Skywalker, who was the Grand Master of the New Jedi Order, when she was elevated to the rank of Jedi Knight. This occurred during the Yuuzhan Vong invasion of the galaxy.
During the knighting ceremony, Jedi Master Skywalker described Jaina as "...a burning brand to your enemies, a brilliant fire to your friends," words that resonated strongly with her. She had been struggling to cope with the ongoing conflict and had been withdrawing from her family and friends.
Nevertheless, Skywalker himself wasn't completely certain about the implications of being the Sword of the Jedi. Throughout the remainder of the Yuuzhan Vong War and in the years that followed, Jaina grappled with the meaning of this title, her destined role, and its potential impact on her life.
The answer presented itself during the Second Galactic Civil War when Jaina's sibling, Jacen Solo, succumbed to the dark side, embraced the identity of Darth Caedus, and seized control of the Galactic Alliance. As Skywalker felt unable to confront Caedus, fearing his own potential descent into darkness in an attempt to avenge his wife, the responsibility passed to Jaina. Only after killing her brother, thereby rescuing the galaxy but also irrevocably altering her relationships with her family, did Jaina believe she had truly become the Sword she was meant to be.