[This is the first in a series of divine attribute summaries I wrote for my systematics class last term.]
Before we can really talk about who God is and what God is like, it is critical that we understand some basic facts about how we talk about God. God is very much not like us. We were created; He created us. We are tiny and physical and very short-lived; God is infinite and eternal and beyond everything else. The gap here is enormous. We must keep this fact in view at all times to avoid reimagining God in our own image. One of the first steps to safeguard our understanding of God is called divine simplicity. Unfortunately, the idea itself is often anything but simple.
Now, when we say that God is simple, we're not really saying anything specific about who or what God is. It's a negation, a way to remind us that God is not something or like something. "God is simple" means essentially that God is not made of "parts". Why? Because God is not made at all. Nothing puts God together out of different components; He simply is as He is. So divine simplicity reminds us that, whatever kind of combination of descriptions you might use to describe God, He's not really combined in any such way. For example, God is not made up of a body and a soul (obviously enough), nor is He made up of some mixture of 50% love and 50% justice, nor any other combination we can come up with. Everything that God is, He is, and is He. God is not just good and true and beautiful; He is goodness and truth and beauty. But we can see that in and for Him, these are not really different things at all.
The point of divine simplicity, then, is to force us to remember at every point that our human concepts we use to describe God, even if they all mean different things as we know them from our experiences of this world, do not in the end point to a God made of different things of different kinds. These concepts can be true when we apply them to God, but in Him they resolve into a perfectly whole unity. So when we start by saying "God is simple," that affirmation about God doesn't itself add new information about God. It sets us on the right track so that each time we do say something about God, we can remember to put it back together in our minds with everything else we have already said about Him. We are reminded to conceive of God not in terms of a collection of independent elements or attributes separate from each other (even just hypotheticaly), but as a pure and indivisible whole of simply Himself.
Of course, this all might raise a question. If God has no kinds of parts at all, and things like His beauty and goodness and justice and power are all simply Him, rather than really different things He has, do any of them mean anything? Well, yes, they do. Even though God is perfectly simple in this way we're talking about, so that all of Him is simply all of Him without parts, the different names and concepts we use for God really make a difference. God is greater than all human comprehension. Our little finite minds, in a world where we are small and everything we see and know is made up of parts, cannot directly imagine what it means for God to be all these things we know He is in such a sublime way that they are all simply Himself. But He reveals Himself precisely in creation, in all the finite things or however many parts they are made. Since God is greater than any of these things, but He made them all, each with some kind of resemblance to Himself, His perfectly simple unity of Himself unveils itself to our minds through millions of different pictures and examples and metaphors in our world. Here we really do see His goodness, justice, etc. all in action in different creatures and different events. The infinite and singular perfection of God, when it shows off in a world of many finite things, necessarily has to "break up" into many types of effects. So God's work in the world really does come to us in objective patterns like goodness and justice and such, but this is because of how the created world is limited, and when we think of God Himself, our job is to remind ourselves at every step that God is simple, so all of these brilliant perfections trace back to the pure, singular, infinite perfection who is the one God.