What does Genesis 4:3 mean?
This verse begins a sentence concluded in verse 4. The first thing we notice is that Cain has a relationship, of some kind, with God. He brings God an offering, the product of his work as a farmer of the fruit of the ground. Even living under the curse and apart from the garden, this second generation of humans continue to see themselves in relationship to God and responsible to Him. God did not completely abandon mankind, and mankind did not turn their backs on God. While the fall ruined our relationship with God, it did not erase it.Again, there are very few details in this part of the Bible. We have no specific knowledge of what Cain's offering was. We have no way to know if God has asked for something in particular, or what kind of attitude Cain had when he brought his gift. What we do know, based on verse 5, is that God is not pleased with what Cain brings. First John 3:12 suggests that Cain was evil, and this had something to do with this incident.
Perhaps Cain was only going through the motions, while Abel was sincerely and humbly honoring God. The fact that Cain responds to God's loving correction in verse 7, makes this a very likely interpretation. Rather than changing his actions to make things right, Cain will respond to God's rejection of his offering with anger and violence.