السَّلَامُ عَلَيْكُمْ

Laa ilaaha il-Allah is made up of two parts:

1. la ilaaha which means to disbelieve in anything that is worshipped besides Allah.
2. il-Allah which means to worship Allah alone

We need both of these things. If we disbelieve in anything that is worshipped besides Allah without worshipping Allah, we end up in atheism. If we worship Allah, but we don’t disbelieve in things that are worshipped besides Allah, we become polytheistic.

Earlier on, we said that the individual words of this statement mean: “There is no god except Allah”
However, this statement is wrong, in a factual sense, because there are many gods that are worshipped besides Allah. For this reason, there is a part of the statement which is understood from the context, and which should read:

“There is no [true] god except Allah”, or
“There is no god [worthy of worship] except Allah”

Sources:

Lecture Notes:
https://www.digitalmimbar.com/AqeedahNotesTimHumble.pdf