The idea behind the "God-shaped hole" is that each person has a void in his life / soul / spirit that can only be filled by the one true God of the Bible. No matter what else a person may try, nothing else fits correctly in this space.
Does everyone have a 'God-shaped hole'?
Ecclesiastes 3:11 says, "[God] has made everything beautiful in its time. Also, he has put eternity into man's heart." God created each person for His purposes and desires a relationship with each one (2 Peter 3:9). He has made His existence evident (Romans 1:19–23). The "God-shaped hole" some talk about is an innate desire in humans to connect with God.
Though we may try to fill this space with other things such as philosophy, hobbies, other people, or other beliefs, nothing fits right except for God. The Bible describes our natural hearts as "deceitful" and says we are unable to completely understand it (Jeremiah 17:9). Solomon writes that our hearts are full of evil and contain madness (Ecclesiastes 9:3). Romans 1:18–23 says we humans attempt to worship just about anything other than God and Romans 8:7 says our natural mind is hostile to God, not wanting to submit to Him and His ways. When we seek to fill our own hearts through human pursuits, we are ultimately left empty and wanting.
It is true that in human pursuits we may find some contentment and even happiness. After all, God did design us for life on earth. But it is only in Him that our earthly activities and relationships best fulfill their purpose. These things could never give meaning to our lives as God can; but in God, our earthly pursuits are a valid and necessary part of living a meaningful life. However, when we look to earthly things, or even other humans, to fill our "God shaped hole," we find that they don't fit quite right and are usually quite temporary.
Solomon, described throughout history as the wisest among people, clearly writes about all pursuits as "vanity," or unsatisfactory. He found only one thing worth pursuing that had lasting, eternal value: "The end of the matter; all has been heard. Fear God and keep his commandments, for this is the whole duty of man. For God will bring every deed into judgment, with every secret thing, whether good or evil" (Ecclesiastes 12:13).
Only a growing, maturing relationship with the God of the Bible, through His Son Jesus Christ, can satisfactorily fill the "God-shaped hole" in each person for this life and throughout eternity.
Can man live without God?
Why did God create humanity?
What does the Bible say about the purpose of man?
How can a person find God? What does finding God mean?
How can I get right with God?
Truth about Humanity