
Allahu Akbar is an Arabic phrase which means "God is Great."
Literally, Allahu Akbar means "Allah is great" but it is usually taken to mean, in the context of the Arab phrase the "Takbir", to mean either "God is Great " or "God is the Greatest".
There are certain problems with the spelling in English of the phrase "Allahu Akbar". The Arab script does not map precisely over the English language (or Latin) alphabet and various different attempts can be made to capture the true sounds. So Allahu Akbar might sometimes be written as Allahu Akhbar for example and there are other variants.
Within an islamic society the phrase can be used often and at many different times. It can simply be an expression of joy. It is also used extensively in prayers. And it has also often been used in battle, as a war cry, which seems to be the use which Nidal Malik Hasan made of it yesterday.
Allahu Akbar can also be used as a fast and colloquial manner of converting to Islam. The simple repetition of the phrase three times, "Allahu Akbar, Allahu Akbar, Allahu Akbar" is taken by most Islamic jurists as being sufficient expression of the core Islamic beliefs that those who say it are now Muslim. Traditionally (and perhaps anecdotally) those who say this either in battle or afterwards when captured will be deemed to have converted, become part of the Ummah (the Islamic community) and thus no longer be considered as enemies.