Allah Akbar and variants (Allahu Akbar is another version) simply means "God is Great!".
Akbar means both 'great' and 'big'
This is like Jesus Saves and John 3:16 for Christians.
These are the first two words of the Muslim call to prayer, usually said as emotively as possible, like Black women singing the national anthem: it is how the Muezzin shows his originality. There are five calls to prayer every day, so it constantly repeated in every Muslim country.
A rather sophisticated Lebanese professor of accounting of my acquaintance thought that the name "Akbar" is a typical name for a hick, like Cletus, Festus, Rastus, or Biggie, the latter being an exact translation.