Classical theologians have long argued that God is simple. That doesn't mean he is easy to comprehend. It means, rather, that he is not composed of any parts whatsoever. Upon first glance, that may seem like an obvious, and not-so-insightful, conclusion. Of course a God who is not a material being is not composed of material parts. You can't "build" God out of various components of matter. Who doesn't already know that?
But the claim for divine simplicity goes beyond the notion of physical composition and affirms that God is not composite in any sense. One implication of this claim is that God's attributes are not concepts that exist outside of him and that he exhibits by measuring up to them. For example, there is no category "goodness" that exists outside of God and to which God measures up by being good. If there were, God would be a personal being distinct from one of his attributes, and by exhibiting a goodness that is defined apart from himself, he would actually be composed, in part, of the attribute of goodness. The same would be true for all his other attributes. In the end, we would end up with a god who was really a bigger version of ourselves: a being who has more of the things we have, but who does not fundamentally transcend us as supreme and absolute over all.
By contrast, consider how the notion of divine simplicity changes our understanding of God's attributes. If God is simple, that means goodness is not a category outside of him to which he measures up. The goodness of God simply is God, viewed from a certain perspective by his creatures. The same would be true for all of his attributes. They are simply ways we limited creatures speak of God himself. God is love. God is holiness. God is wisdom. God is goodness itself.
The doctrine of simplicity has long been a key to the confession of God's absolute supremacy over all and his transcendence of all creaturely existence and categories. When we speak of and encounter God, we are not engaging with a bigger version of ourselves. We are engaging with the One who is utterly unique, absolute, sovereign, and transcendent. Divine simplicity gives us a category of thought by which we can begin to grasp how great he truly is. May it move us to worship.