Honoka is characterized as an ordinary girl. She loves bread, she has average grades at best and most importantly, she loves to have fun. Due to the school being shut down because of low applicants, Honoka determines to save it by creating a school idol club.
This doesn't go as planned, as the early group is faced with no audience on their first "Live", until Hayano arrives and Honoka decides to start their perfomance regardless of how many may watch.
I think these early episodes strongly establish who Honoka is. Determined and motivated, she stands as the visionary of µ's. µ's may be the group without a center, but it undoubtedly has a leader.
Honoka is the driving force of µ's, she pushes everyone forward to their goal and without her, the group would not be able to function.
Pushing herself so hard in order to save the school she starts disregard her health and even her friends, because Honoka thinks that it all depends on her.
Being met with the fact that they were not able to enter Love Live, she experiences frustration and while it may have been enough to save the school, she loses any further motivation to keep going as a school idol.
However, Honoka slowly realizes that there's much more to being a school idol than using it as a means. Honoka had fun. And in reality that's what truly drives her.
Honoka is passion. She loves to sing, she loves to dance and she loves to do it with her friends. Only with the rest of µ's can she truly do what she wants. And only with them can she and µ's be at their best.
This pure passion is what drove µ's further and eventually won them Love Live. Honoka in her passion was shining, and this is what inspired every school idol that came after them.
Being an idol was Honoka's found purpose, though µ's decided to come to an end. And eventually she herself came to terms to that, because she can look back at the fun she had. The legacy and impact µ's left will continue to shine over idol culture regardless.
During the school idol movie Honoka also encounters a strange lady, who may be a symbolic glimpse on what Honoka's adulthood would look like. After all, she still loves what she does and may continue doing it.