“Former Army Chief of Staff Gen. Gordon R. Sullivan has his interpretation. “I don’t know how exactly to spell it, but I know what it means,” Sullivan said. “It means we have broken the mold. We are battle focused. Hooah says Look at me. I’m a warrior. I’m ready. Sergeants trained me to standard. I serve America every day, all the way.’”

On theory is that the word originated with the Second Dragoons in Florida as “hough” in 1841. In an attempt to end the war with the Seminoles, a meeting was arranged with the Indian Chief Coacoochee. After the meeting, there was a banquet.

Garrison officers made a variety of toasts, including “Here’s to luck” and “The old grudge” before drinking. Coacoochee asked Gopher John, an interpreter, the meaning of the officers’ toasts. Gopher John responded, “It means, “How d’ye do.’”

The chief then lifted his cup above his head and exclaimed in a deep, guttural voice, “hough.”

Another theory is that during the Vietnam War many American soldiers used Vietnamese and Vietnamese-French expressions interchangeably with English.

One widely used term was the Vietnamese word for “yes,” which is pronounced “u-ah.” When assigned a task or asked a question, soldiers would often answer with “u-ah.” This term — used for many years after the war by many soldiers, is easily changed to “hooah.”

There are dozens of stories circulating about the etymology of hooah. A popular story among Army Rangers is the following account:

On D-Day, 1944, on Omaha Beach, near the sea cliffs at Point Du Hoc, General Cota, the 29th Division Assistant Division Commander, jogged down the beach toward a group of Rangers from the 2nd Ranger Battalion, and asked, “Where’s your commanding officer?” They pointed him out and said, “Down there, sir.”

General Cota reportedly followed their direction and, on his way down the beach, said, “Lead the way, Rangers!”

The Rangers from 2nd Bat reportedly said, “WHO, US!?” General Cota thought he heard them say “HOOAH!” He was so impressed with their cool and calm demeanor, not to mention their cool term, hooah, he decided to make it a household name.”
Source: http://usmilitary.about.com/od/jointservices/a/hooah.htm