「武」(たけ, take) relates to martial arts - note that “take” is the onyomi and “bu-” is the kunyomi. It’s used in many phrases such as 武士 (busshi, another word for samurai), 武芸 (bugei, martial arts), 武器 (bukki, martial weapons, armor, and all that stuff), 武家 (bukkei, a samurai family), and so on (people were really into the 「武」thing when not being really into it could cost you your life).
The Kumamoto Art Museum (the one abutting Ninomaru) is hosting a collection of 「武」stuff from both the Kato and Hosokawa clans to celebrate the reconstruction of the castle’s keeps, exhibiting the history of Kumamoto Castle and the world of「武」 surrounding it from the castle’s origins in the Momoyama era (1568-1615) through its expansion during the Edo period. Armor and swords related to the Kato and Hosokawa clans are on display along with historical materials such as pictures and ancient documents. Also, swords belonging to the Kikuchi clan and other predecessors of the Higo fief are exhibited. The exhibition will close on 12/15, so you’d better visit soon. - William