Kokonoe is the daughter of two of the Six Heroes, sword-wielding cat-person Jubei and the witch known as Nine. Kokonoe does not directly fight at all. Instead, she spends most of her time working as a scientist under the employ of Sector Seven. She spends most of her time sitting in a lab, conducting experiments, but she often has Iron Tager running around to do errands for her. One scene even shows that she has a sweet tooth, often compulsively holding or sucking on a lollipop.
As a genius, Kokonoe has been involved in quite a lot of projects throughout the BlazBlue canon: she worked with Litchi and Tager on an experiment that accidentally led to the creation of Arakune, she somehow participated in creating the various anti-Sankishin units based off of Saya's DNA (even placing v-13's data into the body of Lambda-11), and even managed to create a giant robotic body for Tager after he had almost been killed during the Ikaruga Civil War.
Somehow, Kokonoe found out that Terumi was behind her mother's death, and while she does support Sector Seven's goal of eliminating magic from the world and replacing it with technology, she also spends a lot of time on her own trying to find ways to kill Terumi once and for all. In Calamity Trigger, she tried to drag Hakumen out of the Edge in order to find a way to seperate him from his SUSANOOH armor, thinking it held a way to stop him. Though she did manage to capture Hakumen after the True Ending, Rachel helped him escape his cell in the start of Continuum Shift's story, so now Kokonoe is juggling several different priorities: recapturing Hakumen, stopping Terumi, and trying to capture Noel Vermillion (because Terumi wants her for some reason).
Kokonoe is was an unplayable character in the BlazBlue series until Chrono Phantasma, in which she was made a DLC character.
"Help Me, Dr. Kokonoe!"
In Continuum Shift, Kokonoe provides "advice" to the characters (and the player, by extension) whenever they achieve the "bad" ending in their story. Directly after the storyline's conclusion, a chibi-fied Kokonoe insults the equally chibi-fied character and breaks the fourth wall by complaining that the player should try the "obvious" route to get to the True Ending and those who are using a flowchart online or trying to get 100% on each character's story should piss off. The sketches have no real connection to the story, though they do occasionally provide an explanation of some background information. However, they mostly serve as extra entertainment.