What Islam teaches
Allah is the Arabic word for God. Not a name for a particular god among several — the word itself is closely related to the Hebrew forms used in the Bible, and Arabic-speaking Christians and Jews have always used it for God, including in Arabic Bibles printed today. Muslims hold that God is one in a strong sense: uncreated, without partner, without offspring, not made of anything, not located anywhere, not male or female, and not represented by any image. This insistence has a name — tawhid — and it is the single most load-bearing idea in Islam.
What you may observe
Mosques with no pictures and no statues, decorated with geometry and calligraphy instead. Muslims who are uncomfortable with a drawing of God in a children's book. The phrase 'God willing' attached to almost any statement about the future, which is a theological reflex rather than a verbal tic.
Why it matters
Because a great deal of what looks like Islamic prohibition follows from it. No images of God, no intermediaries who must be gone through, no priesthood with the power to forgive, no saints who are worshipped. It is also why Muslims react to the suggestion that they worship a different God from Christians and Jews: the claim they are making is that there is only one to worship, so a separate Muslim deity is not a thing they could believe in.
What varies
What counts as an intermediary is genuinely contested. Asking a dead saint to intercede, visiting shrines, or seeking blessing through a holy person is ordinary devotion across much of the Muslim world and is condemned as a violation of tawhid by Salafi and some reformist scholarship. The argument is several centuries old, it is sharp, and it divides Muslims who agree on everything in the first paragraph.
A common misconception
That 'Allah' was originally a moon god. This claim circulates widely in English and has no standing in the scholarship of the languages involved; the crescent arrived as an Islamic emblem with the Ottomans, many centuries after Muhammad. A second misconception is that Muslims are forbidden to use the English word 'God'. They are not, and most English-speaking Muslims use both.
Ask more
If you are reading an argument that turns on what a particular verse says about God, notice which translation it is quoting, and whether it quotes the sentence before and after. That single habit resolves a surprising proportion of them.