If you're asking about why we translate "Allah" as "God", the prevailing theory is that it is because "Allah" is a contraction of the definite article "al" and the indefinite word for god, "ilah". "Allah" is thus simply "The God" and is the word used by Arabic-speaking Christians and Jews as well as Muslims to refer to God.
Are you asking about the word derivation?
The word god is Germanic in origin, and was used to denote any deity. As Christianity was imported into the various Germanic languages the concept of "a god" became "The God." Various forms of God in Germanic languages still remain recognizably related. Including Danish/Norwegian/Swedish (Gud), Dutch/English (God), German (Gott), and Icelandic (Guð).
Arabic of course isn't related to German. It's part of the Afroasiatic language family and is related to Hebrew and other African and middle eastern languages. The exact origin for Allah is disputed but the most common etymology seems to be that its derivative of al-ilah which basically means "the god." It's related to the Aramaic (Elaha) and Syriac (Alaha), which also basically mean "the god" and were (and are) used in Aramaic and Syriac Christian scriptures. It's also related to the El and Elohim words the Jewish people used for God. Along the way "the god" sort of morphed into a personal name, and the famous "there is no god but The God" (la ilaha il al-ilah) turned into "there is no god but Allah (la ilaha illa'llah).
Among people where Arabic is a common language Allah is a personal name for God, and it is simultaneously a word that straight up means God in a generic sense. Allah also has a tendency to be picked up in languages that have significant Muslim populations. Languages have a tendency to pick up vocabulary. English for example sometimes uses the Latin based Divine/Divinity/Deity to refer to God, and we also tend to understand other Latin derived expressions like "dios mio" for "my god." Allah is just one more term among many that is entering European languages as a way to refer to god.