The phrase Allahu Akbar (الله أكبر) can be translated to God is Greater or God is Greatest. In Classical Arabic, when a أَ is added to the beginning of a description it to the English equivalent of adding “est” suffix to the word, or the word “more” before the word. So for instance, the word شَدِيد (shadīd) would be translated as “severe” while the word أَشَدّ (ashadd) would be translated as “more severe” or “severest”. Or another example is while ظَالِم (ẓālim) would be translated as “unjust”, the word أَظْلَم (aẓlam) would mean “more unjust.”
Therefore, the difference between كَبِير (kabīr) and أَكْبَرُ (akbar), is that while the former can be translated as “great” the later would be translated as “greater”. So however much great كَبِير (kabīr) is, أَكْبَر (akbar) would be greater. A good example of this is in the following verse:
[2:219] They ask you about intoxicants and gambling: say, “In them there is a gross sin, and some benefits for the people. But their sinfulness far outweighs their benefit.” They also ask you what to give to charity: say, “The excess.” GOD thus clarifies the revelations for you, that you may reflect,
يَسْأَلُونَكَ عَنِ الْخَمْرِ وَالْمَيْسِرِ قُلْ فِيهِمَا إِثْمٌ كَبِيرٌ وَمَنَافِعُ لِلنَّاسِ وَإِثْمُهُمَا أَكْبَرُ مِنْ نَفْعِهِمَا وَيَسْأَلُونَكَ مَاذَا يُنْفِقُونَ قُلِ الْعَفْوَ كَذَٰلِكَ يُبَيِّنُ اللَّهُ لَكُمُ الْآيَاتِ لَعَلَّكُمْ تَتَفَكَّرُونَ
The expression Allahu Akbar can be found twice in the Quran, once in 40:10, and the other time in 29:45. While 40:10 is in the context of God’s abhorrence being greater towards the disbelievers than the disbeliever’s abhorrence towards themselves, and does not match how the expression is commonly used like during Salat, the other occurrence in 29:45 is actually used in the context of Salat.
[29:45] You shall recite what is revealed to you of the scripture, and observe the Contact Prayers (Salat), for the Contact Prayers prohibit evil and vice. But the remembrance of GOD (through Salat) is the most important objective (*greatest). GOD knows everything you do.
اتْلُ مَا أُوحِيَ إِلَيْكَ مِنَ الْكِتَابِ وَأَقِمِ الصَّلَاةَ إِنَّ الصَّلَاةَ تَنْهَىٰ عَنِ الْفَحْشَاءِ وَالْمُنْكَرِ وَلَذِكْرُ اللَّهِ أَكْبَرُ وَاللَّهُ يَعْلَمُ مَا تَصْنَعُونَ