that's the optional minigame battle component. if you want to do well in it and improve character stats, you have to go through separate missions and train your character.
if you lose, you're given a really humiliating title.
http://key.visualarts.gr.jp/newsoft/index.htm
character profiles (wikipedia copypaste)
Riki Naoe (直枝理樹, Naoe Riki?)
Riki is the male protagonist of Little Busters! He is a member of the Little Busters, and of them, he is seen as the only one that is straightforward and has common sense. His parents died when he was very young.
Komari Kamikita (神北小毬, Kamikita Komari?)
Komari is the main female heroine in the story. She is very childish, taking great interest in fairy-tales, picture books, and candy. She is very clumsy. Voiced by: Natsumi Yanase
Rin Natsume (棗鈴, Natsume Rin?)
Rin is the younger sister of Kyousuke Natsume. She is anti-social and is usually seen alone. She does not communicate well and is seen as inarticulate. Voiced by: Tomoe Tamiya
Haruka Saigusa (三枝葉留佳, Saigusa Haruka?)
Haruka is a schoolmate of Riki's from a different class, but despite this, always seems to find time to hang around in Riki's classroom. She is a problem child and will start an uproar for her own personal enjoyment. Voiced by: Keiko Suzuki
Kudryavka Noumi (能美クドリャフカ, Nōmi Kudoryafuka?)
Kudryavaka, also known as "Kud" (クド, Kudo?) for short, is a girl who is not fully Japanese. Her grandfather was Japanese, and per his influence on her, she came to know much about the Japanese culture, including the language. She is very bad in English, though. Voiced by: Akemi Kaneko
Yuiko Kurugaya (来ヶ谷唯湖, Kurugaya Yuiko?)
Yuiko is Riki's classmate who has a self-sufficient personality. She is sometimes seen carrying a katana. Voiced by: Ryōko Tanaka
Mio Nishizono (西園美魚, Nishizono Mio?)
Mio is a calm girl who is very dilligent. She is always seen with a parasol when outside. She enjoys boys love series. Voiced by: Yūmi Arai
other info
scenario writers:
maeda jun (the writer for the main stories for air, clannad, and tomoyo after) : all the male characters and natsume rin. also game concept and planning was organized by him. this is the last game that he will be writing for.
tonogawa hayato: kamikita komari, kurugaya yuiko
gashida reo: nishizono mio
jokiri o: saegusa haruka, nomi kudryavka
character designers
na-ga: male characters, rin, kudo, mio
itaru (traditional key genga/character designer person): komari, haruka, yuiko