Romans 1:20 states, "For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse."
This verse tells us that two things are clearly seen about God in creation. The first revelation is of an eternal power. That is, there must have been a power sufficient to create the universe we see and that power must have preceeded the universe we know and could have nothing preceeding it--that is, it must be eternal.
It is important to note that the first revelation (of an eternal power) does not require a personal God. It could be fulfilled by an impersonal force. Therefore, Paul points out a second revelation that can be seen in creation--the Godhead. The word, Godhead, is found only three times in the Bible: Acts 17:29; Romans 1:20; Colossians 2:9. It does, as you mention, refer to the three-in-one God. However, it is in no way a synonym for trinity. The word does not mean trinity.
The word, Godhead, refers to the person of God or we might better say the divine personality. In Acts 17:29, we read, "Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man's device." The Godhead is contrasted with a lifeless image made by man's device. The Godhead is not a lifeless image. He is a living being. As stated in this verse, we are His offspring. How could the one who created thinking, feeling beings be an impersonal force? He could not.
That is the essence of what is being taught in Romans 1:20. Not only does creation show that there must be an eternal power behind all things, creation also shows the touch of a personal deity. He thinks, He loves, He creates, He designs. How do we know this from creation? I already mentioned the existence of man. If man can think, dream, love, hate, feel, appreciate beauty, and much more, how could his Creator be nothing more than an impersonal force?
But there are other evidences. Design is an attribute of personality and this world shows multiple examples of God's designing hand. More than that, we see His love for beauty and variety. Psalm 104:24 states, "O LORD, how manifold are thy works! in wisdom hast thou made them all: the earth is full of thy riches." The word, manifold, means many-folded and refers to the variety of creation. The wisdom of God's works refer to their quality. The earth being full of God's riches refers to the great quantity of created things. Infinite variety and design do not indicate an impersonal power, but rather a personal God. It points to a Godhead.
