What is God?
God is Spirit, infinite, eternal, and unchangeable, in his being, wisdom, power, holiness, justice, goodness, and truth.
Exodus 34:6-7 (NASB)
Then the LORD passed by in front of him and proclaimed, “The LORD, the LORD God, compassionate and gracious, slow to anger, and abounding in lovingkindness and truth; who keeps lovingkindness for thousands, who forgives iniquity, transgression and sin; yet He will by no means leave the guilty unpunished, visiting the iniquity of fathers on the children and on the grandchildren to the third and fourth generations.”
Exodus 34:6-7 is one of my favorite passages in all of Scripture, which includes the story that proceeds and follows. When Israel proclaimed the proper name of their God (Yhvh i.e. יְהוָֹה Yehovah or יַהְוֶה Yahveh ) they were invoking the nature of God, given to Moses on Mount Sinai.
John 1:17-18 (NASB)
For the Law was given through Moses; grace and truth were realized through Jesus Christ. No one has seen God at any time; the only begotten God who is in the bosom of the Father, He has explained Him.
In the words of the prologue to his gospel, John is pointing to the man Jesus as God in human flesh. He does this by using the picture of Exodus 34:6-7 in his proclamation about Jesus. How can that which is Spirit, infinite, eternal, and unchangeable, in his being, wisdom, power, holiness, justice, goodness, and truth become flesh? This is the question that caused the Arminian controversy; the heresy that says that Jesus is a created being and not God.
John 14:7 (NASB)
If you had known Me, you would have known My Father also; from now on you know Him, and have seen Him.”
To answer the question what is God, God became flesh in the person of Jesus Christ and dwelt amongst us. (Jn 1:14) What is God? The person of Jesus Christ has explained him. (Jn 1:18) “He is the image of the invisible God, the firstborn of all creation.” (Col 1:15,NASB) And He is the radiance of His glory and the exact representation of His nature, and upholds all things by the word of His power. When He had made purification of sins, He sat down at the right hand of the Majesty on high, having become as much better than the angels, as He has inherited a more excellent name than they.” (Heb 1:3-4, NASB)
 The Shorter Catechism, Question 4.