"If you continue and don't give up, your wish will be granted."
Yoshino Kouko (originally Ibuki Kouko) is a recurring minor character in Clannad. Though she has no backstory of her own, she's involved in Fuko's story (she's present in Episode 6 to 9 of Clannad) and in her husband Yuusuke's backstory (shown in Episode 12 of After Story). She appears a few other times as well (such as the show's final scene).
Kouko is a soft-spoken woman who is often smiling. She's optimistic, and she does her best to support all her friends and family, most especially Fuko and Yuusuke. Her love for others is powerful, to the point of almost foregoing her marriage to be able to better take care of her comatose sister. Her patience and encouragement of others served her well during her years as an art teacher at the high school. Maturity and politeness are values she wants to stress, particularly for Fuko (who can at times be lacking in both). Overall, then, Kouko is a woman who thinks positively, cares for others, and pushes them to be the best they can be. You can see this when Nagisa and Tomoya invite her to the school's Founder's Festival:
Kouko is first seen as one of the customers of the Furukawas' bakery, who Tomoya meets as he watches over the store following on of Sanae's bread breakdowns. Later on, Tomoya learns that Kouko used to be the art teacher at the high school; even more importantly, she's Fuko's older sister, the one whose wedding Fuko is promoting. In another twist of coincidence, it turns out her fiancee is none other than Yoshino Yuusuke, an electrician whom Tomoya met during a random encounter on the street. (He's also a musician the Sunoharas love.)
After learning that Kouko is Fuko's sister, Nagisa and Tomoya visit her multiple times. She remembers Nagisa from her last year of teaching (even though Kouko stopped teaching the year before the story began, since Nagisa is repeating a year, she had her as a teacher). Nagisa and Tomoya learn Fuko's backstory: she was a girl who often played by herself and didn't make many friends. At one time, Kouko tried to force Fuko to get friends by giving her the cold shoulder, but that wasn't very effective. On her first day of high school, Fuko was hit by a car, and she's been in a coma ever since (three years). Kouko visits her often and does her best to take care of her. She even ponders foregoing her marriage to Yuusuke (which is a secret that Fuko informed Nagisa and Tomoya of) in order to take better care of her sister.
The two convince Kouko to come to the school's Founder's Festival in order to talk with her sister, but it's to no avail: she can't see Fuko. Thankfully, though, they're able to convince Kouko that what Fuko would want is for her to get married, and she decides she wishes to be married on school grounds. Nagisa and Tomoya go to Koumura for assistance there as people begin to forget Fuko.
Soon the day of the wedding arrives, and it goes off perfectly: it's held on school grounds, and countless guests are there thanks to Fuko's starfish. As the newly wedded couple comes to Nagisa and Tomoya, by a supernatural happenstance, Fuko is able to tell her sister congratulations on her wedding, just as she wanted to. (Kouko appears at about 3:45 in this video.)
After this, Kouko is basically relegated to the background until After Story. Now known as Yoshino Kouko instead of Ibuki Kouko, she appears with her husband at the baseball game. She next appears during Shima's arc. While Shima is dressed as a girl, he runs into Kouko in the halls (since she's an art teacher), and she allows him to see Misae at the student council meeting.
Her next main role appears when Yuusuke is telling Tomoya his backstory. He was a student when Kouko was a teacher, and they grew close. After he graduated, as he was heading off to become a musician, he swore he'd become famous, and he asked if she'd go on a date with him when he returned. She accepted his offer. During his tumultuous time as a rock star, he eventually hit bottom and returned home, only to serendipitously run into her outside the train station. He realized that she was the one he should have been focusing on, and he collapses into tears in front of her. She encourages him and offers him support, telling him to persevere and not give up, and that eventually led to their dating and getting married.
She next appears again 7 episodes and 5 years later. Tomoya and Ushio are walking by a park and see her and (lo and behold!) Fuko, woken up after all these years. She introduces herself to Ushio and tells her she'll grow up to be cute and strong like her mom. She then introduces Fuko as well, leading to an interesting friendship between her and Ushio.
Finally, Kouko appears for the last time during the final scene. She's walking with Fuko to the hospital to get a check-up (after being in a coma for about 10 years, you'd need check-ups too!), and they're having a cheerful walk, Fuko being childish as ever. Suddenly, Fuko glances into the forest and starts up a strange conversation that Kouko can't make heads or tails of. Eventually, Fuko just runs into the forest, leaving Kouko confused and dumbfounded.
Effect on Main Plot
Kouko helps Nagisa and Tomoya's relationship in a few, kind of indirect ways. For one, she provides the goal for Fuko's starfish quest; without her, Nagisa and Tomoya would have never met Fuko, and their time with her is a big help in building up their fledgling relationship. Kouko is also the one who supported Yuusuke; without her support, who knows what would have become of him? His being supported his a good thing, because he is a wonderful mentor for Tomoya in After Story. She also (re)introduces Fuko to Tomoya and Ushio. This provides Ushio with what appears to be her first real friend, which must make Tomoya glad (I have a feeling that having a friendless child would make you worried for her).
Kouko is also an effect in an even less direct way: she's somewhat of a foreshadowing of Nagisa. Liam Francis Traveller drew my attention to this aspect in his post on Fuko's arc: Kouko is a strong, caring woman whom Nagisa knows and who sort of looks like Nagisa. Both her personality and looks bear some resemblance to Nagisa (Liam says she looks like an older Nagisa, and the resemblance is definitely more blatant when looking at Nagisa at the end of the show). It's interesting to see that this woman who resembles Nagisa also have some aspects of her relationship with her husband resemble Nagisa's: she's an older woman who helps support a guy with some delinquent tendencies and inspire him with self-confidence and courage. There are definitely some interesting correlations between Kouko and Nagisa.
Once again, the big theme is family. Most of the times we see Kouko are because of her connection with Fuko. Her familial love with Fuko is a two-way street, even if it might not seem like to Kouko for a while. Kouko cares for her comatose sister for over two years with no sort of loving response from her (because it's simply not possible). Even with no possible encouragement from Fuko, Kouko still goes to visit her and care for her; she perseveres in it (and it's self-sacrificial as well). Through that supernatural occurrence, though, Kouko is able to receive a loving message from her sister; all the work that Fuko puts into making the wedding a success could almost be viewed as her thank-you gift to Kouko for all the caring she has had over the years, even if Fuko doesn't consciously talk about being in a coma.
Kouko also offers Yuusuke the advice to persevere, as the quote that started this post attests to. (The inspiration of others with advice such as this seems to be a common event in Clannad, even from the very first scene.)
There's only so much to say about a character like this. She has no real backstory: she just plays parts (at times crucial ones) in other people's backstories, like Fuko and Shima and Yuusuke. Sometimes she just seems like an accessory to Fuko: if Fuko weren't there, she wouldn't be there. It's almost like Kouko is a contingent character, depending on Fuko and Yuusuke to exist (in the show). Actually, Yuusuke almost seems like a contingent character dependent on Kouko (would anything have come of that random encounter with Tomoya if he weren't Kouko's fiancee?); so one way to say it would be that Yuusuke is dependent on Kouko, who is in turn dependent on Fuko. So it all rests on Fuko: that just goes to show how important of a character she really is.
That's mostly all I have to say about that: Kouko is sort of a support character for Fuko and the gateway (and sometimes a support character) for Yuusuke, plus she's also a bit of an alternate Nagisa. But above all, she's Fuko's sister, and a antithetically mature one too (she's sort of the Mei to Fuko's Sunohara, in a way).
Thanks for reading. God Bless, and peace.
Nota Bene: All clips are from the Clannad Central YouTube channel run by the Clannad (クラナド/Kuranado) fan page on Facebook. All character themes and other music from the show can also be found on said fan page, in the music player. My gratitude to them and all the work they do.