allah akbar means god is great. it started when the first mosque was built (I guess shortly after Muhammed died, maybe sometime in 600 AD?) and they wanted to call everybody into the mosque because it was time to pray.
Allahu Akbar means "God is great" but it is used to mean different things for different occasions. In an affirmative statement like at a protest or celebration it means exactly what it says, but in some cases it is used in the same way we Americans will say "oh my god!" as an expression of awe or disbelief.