These games are based on the anime Ikki Tousen (一騎当千 Ikkitōsen, lit. "Strength of a Thousand"), known in North America as Battle Vixens, which is in turn based on a manga series written and illustrated by Yuji Shiozaki, which is even more tenuously based on the classic Chinese novel Romance of the Three Kingdoms.
The series revolves around an all-out turf war in the Kanto region of Japan where fighters known as Tōshi (闘士), meaning "fighting soldier," from seven schools battle for supremacy. The story centers on Hakufu Sonsaku, a fighter who transfers to Nanyo Academy, one of the seven schools involved in the turf war.
Source: Wikipedia, "Battle Vixens", available under the CC-BY-SA License.
The games are generally about fighting but really revolve on the introduction of new characters.