Al is The. Its used in the arabic language for most words, Al-Mu'alima- The teacher.
Though in reference to God it is used to emphasis a superlative word. Like saying, The King, The one, The beneficial etc
So the word Allah altogether, also according to what you have said should mean. The God(Ilah), which announces that there is only One and He is the greatest.
This is also explained in the term,
La(no)-ilahha(God other)-illa(then)-allah.(The God- one and only.)