Answer:
Supposedly it comes from the abbreviation "HUA," meaning Heard-Understood-Acknowledged, but it's most likely just something used to give motivation, since Marines are notorious for being motivated.
Hoorah, hurrah, hooray, hurray are variants which all mean agreement, approval, celebration or just plain happiness. The etymology is a mystery, but these words are found in written English at least a century before the establishment of the USMC which casts considerable doubt on the HUA explanation.