Official definition, as listed on a T-shirt
my brother graciously purchased for me upon his graduation from boot camp
at Fort Jackson
(for we all know that Webster gets all his definitions from various screen printed clothing items):
Hooah: /who.aah/ n/adj/vb/advb/etc. (of US Army origin). Refers to and means anything except no; slang used by hardcore soldiers; agree; disagree, but I will do it anyway; alright; cool; aloha; stop whining; roger; see ya later; what to say to a drill sergeant or commander when not sure of an answer; all is good; and of course...I love this job!