The Takbīr or Tekbir (تَكْبِير) is the Arabic name for the phrase Allāhu Akbar (الله أكبر). Usually translated "God is [the] Greatest," or "God is Great", it is a common Islamic Arabic expression, used as both an informal expression of faith and as a formal declaration.
The form Allāhu is the nominative of Allah "[the one] God".
The form akbar is the elative of the adjective kabīr "great". As used in the takbir it indicates the superlative (best), usually translated as "greatest". The term takbīr (تَكْبِير) itself is the stem II verbal noun (tafʿīlun) of the triliteral root k-b-r "great."
In the English version of Ibn Qayyim's book "The Way to Patience and Gratitude", it is stated in the footnotes that "Allahu Akbar" translates into "Allah is Greater". In the Second Edition on page 463, it quotes:
"...I preferred using 'the Greater' to the 'the Greatest', as it is commonly used. Allahu Akbar literally means, "Allah is Greater" with the comparative mode. Yet, this does not mean that He (Glory be to Him) is not the Greatest, nor does it mean that there is anything that is put in comparison with Him. This is because when the Muslim says it, he means He is "Greater" than anything else, which, consequently, means He is the Greatest. This use gives more influence. This may be why it is used in Arabic this way, otherwise it should have been used as "Allahu al-Akbar", in the superlative mode. Surely, Allah Knows best. (Translator)..."
See also: Lebaran, Hari Raya, Ramadan Gift