What does Romans 1:18 mean?
This verse begins a longer section describing God's attitude and actions toward human sinfulness. These verses could be considered an answer to the questions, "Why is the gospel such a big deal? Why do human beings need to be declared righteous by God? What do we need to be saved from?"The previous verse showed that God declares righteous those who come to Him by faith. Later Paul will show that faith must be in Christ and His death for our sins on the cross. Now, though, he shows God's attitude to those who don't come to Him by faith in Christ.
Instead of God's righteousness, it is His wrath—God's righteous anger and judgment—that is revealed against sin. God's wrath comes from heaven, from His essential nature and existence, not some created thing or place. God is angry against human ungodliness and unrighteousness. Human beings, apart from God, use their lack of righteousness, their sinfulness, to suppress or hold back the truth about who God is.
Unrighteous people—which includes all of us by nature—don't want to know what is true about God, and they don't want others to know or believe that, either. This verse is extremely important for understanding why some people seem so resistant to belief. In short: they don't believe because they don't want to. The problem is not that truth is unavailable; the problem is that truth is being suppressed.