I don't know. Just did a search and there is no solid history of it. Here is my favorite explanation from Wikipedia.

"The term may have been derived from the Turkish phrase "vur ha!" translated as "strike!" or "kill them all!", which was used as a battle cry at the Ottoman Empire army and adopted as a Russian battlecry "Urrah!"

Not sure how true that is, but it sounds cool.

It can be used in many ways.

"Marine, go fix that truck."
"Oorah."

"Lets go kill the bad guys, oorah?"
"Oorah!"

Oorah, meaning hello. Two Marines passing each other. "Oorah." "oorah"

Excited, "Oorah!"

The list goes on.