The regular Arabic adjective has two forms, fa3eel and af3al. fa3il is the normal form, whereas af3al is the increased form. (There also are feminine forms, and words with different morphology, but two point is: whereas English has 3 forms: great, greater, the greatest, Arabic has only two).
For example, "kabir" is fa3eel and means great. Its af3al is "akbar". If it stands alone, it means "the greatest". It only means "greater" if a comparison is induced by the preposition min.
So, "Allahu akbar" means "God is the greatest". But "Allahu akbar min ash-Shaitan", for example, means "God is greater than Satan".