Allah o Akbar means Allah is Great. Greatest of All. The Great Allah.
When we hear Allah o Akbar in Call for Prayer (Aazaan) it refers to the fact that Allah is Great amongst all, so whatever we are doing is not worthy continuing anymore, need to leave whatever we are doing at that time (even if Reciting Quran Majeed) and listen along with answering the Call for Prayer.
I am depressed and my heart is soft, better to cash the softness of heart so need to say Allah o Akbar, Ya Allah you are above all. Ya Allah! my depression is big but you are the Greatest, above everything that exists – Your Creations.
While being stuck in legalities, need to get signatures from dozens of ministries, offices and government sectors and thinking these people are great as people like us need to ran after them. Say NO, Allah is The Great. So next time we are waiting for the one to get our documents signed we need to remind ourselves by repeatedly saying Allah o Akbar, Allah o Akbar, Allah o Akbar.
Ya Allah, make us Muslims to remember in every fraction of second in our lives that Allah is Great, Greatest among all. Aameen