First, it means we cannot posit a distinction between God and His attributes the way we might between a creature and its attributes. A man, for instance, may be wise, just, and powerful. But he is not identical with the wisdom, justice, and power by which he is such. Each of these is a part that contributes some form of being to him, and each is distinct from the man as a whole. He depends upon these qualities to be as he is. Because God is simple, this is not how He has His attributes. Properly speaking, God does not have wisdom, justice, power, and so forth—attributes really distinct from His being as God. Rather, God just is the wisdom by which He is wise, the justice by which He is righteous, and the power by which He is powerful, and so forth for all His other attributes.
Second, and more deeply, divine simplicity means that God is not composed of existence and essence. As with His attributes, God does not have existence or essence as principles really distinct from His being as God. Rather, God just is the act of existence by which He exists and the essence of divinity by which He is God. But this is not how it is with creatures. To be a human, for example, is to be a certain kind of creature. But no human being is humanity as such. Rather, each one possesses humanity as a principle determining him to be the kind of being he is. Moreover, being a human does not explain why any particular human exists. Rather, each man’s act of existence is a principle he possesses in addition to his essence. In short, it is not the essence of humanity to be. For classical theists, this is the proper locus of the Creator-creature distinction. Creatures possess existence as a gift (see Acts 17:25, 28; Rev. 4:11) that is really distinct from their respective essences, whereas God simply is His own existence, there being no composition of principles of existence and essence in Him.
All that is in God is God. He, being His own existence and essence, and so not derived from causes as are all other beings, is alone adequate to ultimately account for all that is caused-to-be. He is the One from whom, and through whom, and to whom are all things (Rom. 11:36). This identifies Him as the lone worthy object of all our worship and gratitude. All things look ultimately to Him for their being, but He looks to none. While divine simplicity is not the only way to characterize the Creator-creature distinction, it is a doctrine without which the distinction becomes nearly impossible to maintain. It helps us see why God cannot be reimagined as a super-angel even though angels are immaterial beings of immense power, glory, and holiness. An angel, no matter how magnificent, still depends upon principles of being more primitive than itself and so clearly is not the first cause and Creator of all things. The classical doctrine of divine simplicity deserves renewed attention from modern Christians as we seek to be ever watchful in maintaining the Creator-creature distinction and in giving to God alone the worship that is due Him.