Natural theology is the study of God through observing nature and using reason. Rom. 1:20 says, "For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse." The Bible tells us that God can be seen and understood by looking at creation. After all, it is God who made the heavens, the moon, and the stars (Psalm 8:3, 33:6), and the heavens declare His glory (Psalm 19:1). Just as a painting reflects the painter's ability, the order, majesty, and balance found in nature show the great ability of God. The universe is immense, balanced, and wonderful. This did not happen by accident any more than the balance and precision of a watch suggest it was formed by accident.
But the darkened heart and mind of sinful man means that even though it is evident that God can actually be detected through what is around us that some suppress the truth of God in their unrighteousness and deny what nature itself can teach us. Romans 1:21-23 further says, "For even though they knew God, they did not honor Him as God, or give thanks; but they became futile in their speculations, and their foolish heart was darkened. 22 Professing to be wise, they became fools, 23 and exchanged the glory of the incorruptible God for an image in the form of corruptible man and of birds and four-footed animals and crawling creatures."
It is from such hardness of heart and mind that other errors about God have been invented. Pantheism teaches that God and nature are the same thing, thus denying the distinction between Creator and creation. Panentheism says that the universe is contained within God's nature. Both pantheism and panentheism deny the transcendent nature of God by denying that He is completely "other" than His creation.
So, natural theology is the study of God that we can conduct by looking at the wonders and beauty of creation.