The phrase Allahu Akbar (الله أكبر) is a common phrase used by Muslims in various situations, including the Salah (obligatory five prayers a day) and has even been used in the past by some non-Muslims as a show of support or in reference to the common Abrahamic god. It is widely conflated with the Muslims who shout it whilst engaged in Jihad. The literal translation of this phrase from Arabic means "God is greater!" The phrase has a unique history in scripture and its early use and conception.
Difference between Allah and Ilah
Allah = الله (alif ا, lam ل, lam ل, ha ه)
ilah = اله (alif ا, lam ل, ha ه)
Transliteration: ašhadu ʾanla ilāha illal-Lāh, wa ʾašhadu ʾanna muḥammadan rasūlul-LāhLiteral: There is no god but Allah and Muhammad is the messenger of Allah.
The phrase is commonly mistakenly translated to "There is no god but God." However, in Islam the name Allah as a proper noun, as opposed to a common noun descriptive applicable to any deity. Allah is not the generic word for 'god' in Arabic, but the name of Islam's deity.
A Treatise on Maliki Fiqh (Including commentary from ath-Thamr ad-Dani by al-Azhari)(310/922 - 386/996)
Is Allah the same as God?
In another case in Malaysia, the government banned Christians from using the word 'Allah' in reference to the Christian God, and in one incident, reported by CNN in October of 2009, twenty-thousand Bibles were seized by authorities because they referred to the Christian God as 'Allah,' completely disregarding the fact that due to the evolution of the Malay language, which has borrowed extensively from Arabic, Sanskrit and Portuguese, there is no indigenous Malay word for 'God' other than the pagan 'Allah'. It was reported that in 2010 a court ruling overturned the ban, a decision which the government has appealed against, insisting that it should remain in place. This decision to allow Christians to use the word 'Allah' has led to violent protests and bombings of several Malaysian churches. One of the protesters summed up the thoughts of many Malaysian Muslims, stating, “Allah is only for us, The Christians can use any word, we don’t care, but please don’t use the word Allah.”
So, according to Muslims, is 'Allah' the word for 'God' or the name of their particular deity distinct from the God of Christianity and Judaism? No doubt you will receive very different answers depending on the situation. However, the original Arabic script found within the Qur'an tells you all that you need to know.
Claim: 'Akbar' means 'great.'
Fact: 'Akbar' in English is translated 'greater,' not 'great.' Great = كبير (Kebir)
Greater = أكبر (Akbar)
Kebir and akbar are not interchangeable words. For evidence, we only need look to the Qur'an. Both kebir (great) and akbar (greater) are used in the following verse:
يسالونك عن الخمر والميسر قل فيها اثمتتفكرون كبير ومنافع للناس واثمهما اكبر من نفعهما ويسالونك ماذا ينفقون قل العفو كذلك يبين الله لكم الايات لعلكم
Yas-aloonaka AAani alkhamri waalmaysiriqul feehima ithmun kabeerun wamanafiAAu lilnnasiwa-ithmuhuma akbaru min nafAAihima wayas-aloonaka mathayunfiqoona quli alAAafwa kathalika yubayyinu Allahulakumu al-ayati laAAallakum tatafakkaroona
Yusuf Ali:They ask thee concerning wine and gambling. Say: "In them is great sin, and some profit, for men; but the sin is greater than the profit." They ask thee how much they are to spend; Say: "What is beyond your needs." Thus doth Allah Make clear to you His Signs: In order that ye may consider- 
Lane's Lexicon and Other Sources
Lane's Lexicon, the most revered and scholarly dictionary of the Arabic language, confirms the majority view is that "Allahu Akbar" refers to Allah being "greater". Unlike in its early years, so does Wikipedia, stating the phrase literally means "God is greater". But is usually translated "God is [the] Greatest," or "God is Great". Similarly, Pierre Tristam, the Lebanese-American About.com Guide states, although most often translated as "god is great," Allahu Akbar is Arabic for "god is greater," or "god is greatest." Many news sources and other web resources are now also beginning to use the more correct translation.
Used in Context by Muhammad
One must also note that if the word "Allah" meant "God", why then would he be telling the Jews of Khaibar (who supposedly worship the same god) that Islam's Allah is greater?
Here are a few more quotes which use the phrase "Allahu Akbar".
Al-hamdu lillahi-lladhi hadana wa at amana wa saqana wa naamana. Allahu akbar. Allahumma'l fatna nimatik bi-kulli sharr. Fa asbahna minha wa amsayna bi-kulli khayr. Nasaluka tamamaha wa shukraha. La khayr illa khayruk. Wa la ilaha ghayruk. Ilaha'-saliheen wa rabba'l-alameen. Al-hamdu lillah. Wa la ilaha illa'llah. Ma sha'Allah. Wa la quwwata illa billah. Allahumma barik lana fima razaqtana. Waqina adhaba'n-na
- Allah - A hub page that leads to other articles related to Allah
- Islamic Terms - A hub page that leads to other articles related to Islamic Terms
- Allahu Akbar - Muslim Arabic speaker, commenting on this page, confirms "Allahu Akbar" means "Allah is greater" (not "God is great)"
- "Malaysia: Government Maintains Only Muslims Can Use ‘Allah’ Term" - Compass Direct News, January 08, 2008
- Saeed Ahmed - "Bibles seized as Malaysia minorities fear fundamentalism" - CNN, October 29, 2009
- Mydans, Seth. "Churches Attacked in Malaysian ‘Allah’ Dispute", The New York Times, January 9, 2010.
- Quran root browser - ك ب ر - k-b-r
- "Takbir", Wikipedia, accessed August 4, 2013 (archived), http://en.wikipedia.org/wiki/Takbir.
- Pierre Tristam, "Allahu Akbar", Middle East Issues (About.com), accessed August 4, 2013 (archived), http://middleeast.about.com/od/a/g/allahu-akbar-definition.htm.
- Ludwig W. Adamec, "Historical Dictionary of Islam", Scarecrow Press, 2nd ed. 2009, p. 32