Allah is simply the Arabic word for 'God'. It is a name by which Muslims and even Arab Christians call him. 

"Allah" is one of the names that God has mentioned for himself throughout his revelation. These names are descriptive definitions of his divine essence and holy attributes. For example, the most gracious (ar-rahman) and the most merciful (ar-Rahim), refer to his infinite kindness and mercy.

Allah said in his book:

He is Allah, besides whom none has the right to be worshipped but he. (he is) the king, the holy, the one free from all defects, the giver of security, the watcher over his creatures, the almighty, the compeller, the supreme. Glory be to Allah! (high is he) above all that they associate (with him). He is Allah, the creator, the inventor of all things, the bestower of forms. To him belong the best names. All that is in the heavens and the earth glorify him. And he is the all-mighty, the all-wise.

(surah ahashr:23-24)