Meaning of la ilaha illa Allah
The true meaning of la ilaha illa Allah is detailed. It means linguistically that there is no god besides Allah. The true meaning of this statement is that no one has the right to be worshiped except Allah.
So the meaning of la ilaha illa Allah is that no one deserves to be worshiped except Allah. That is an essential part of Islam. It involves rejection of false gods and submission to Allah.
The pronunciation of la ilaha illa Allah is part of the Shahada. La ilaha illa Allah is the first part of the complete pronunciation of the Shahada.
Thus, in order to validly pronounce the statement, one must, among other things, reject all false gods. That concept is called Kufr bi Taghut. Then one should worship Allah alone, and that is done by making Him One in His Names/Attributes, Dominion and worship. You can learn more about that in the topic of Tawheed.