What does that mean?
Most every person is born a citizen of a political state or country where they have identity, rights, protections, and share in a certain culture, mores, and values. Additionally, we are told in the Bible that each person is also born into the kingdom of this world where Satan rules (2 Corinthians 4:4) and is therefore enslaved as a member of that culture, taking part in Satan's values and practices—namely rebelling against God (Romans 6:16; Genesis 3:1; 1 John 2:16).
This is the sin we are born into and remain captives of until we are rescued and redeemed by Jesus (Ephesians 2:1–5). When we join the kingdom of God through the grace of Jesus and the power of His resurrection, our citizenship is transferred from the world ruled by Satan to the heavenly kingdom ruled by God (John 3:3). Philippians 3:18–21 describes this concisely: "For many, of whom I have often told you and now tell you even with tears, walk as enemies of the cross of Christ. Their end is destruction, their god is their belly, and they glory in their shame, with minds set on earthly things. But our citizenship is in heaven, and from it we await a Savior, the Lord Jesus Christ, who will transform our lowly body to be like his glorious body, by the power that enables him even to subject all things to himself."
The Bible tells us that our entry into this heavenly citizenship is like being born again (John 3:3; Matthew 3:2; 7:21; Romans 14:17). The Gospels record Jesus speaking of the kingdom of heaven repeatedly. He likened it to a field where wheat and weeds grew together, appearing similar. Jesus said the two would be identified and separated at harvest (Matthew 13:24–30). God knows the difference between those who belong to Him and those who only appear to. There are those who act like citizens of heaven, but have no relationship with Jesus and have not experienced a rebirth in their hearts (Matthew 7:21).
When we are reborn into the kingdom of heaven we are also made into a new creation (2 Corinthians 5:17) by the Holy Spirit's indwelling (John 14:17; 1 Corinthians 6:19–20; Ephesians 1:13–14). He then begins His work of transformation replacing worldly desires with godly desires, making us more like Jesus (Romans 12:1–2; 8:29). It is through the Holy Spirit's work that we are empowered to make decisions that reject the values of the world and practice those which honor God (1 John 2:15–17). Matthew 6:19–20 tells us that we can store up treasure in heaven. Additionally, as citizens of heaven, we are given the role of ambassador to others until we are recalled, in a way, back home (Ephesians 2:18–19; 6:20; 2 Corinthians 5:20–21).
Our time on earth is relatively short compared to eternity. We are called to live here as strangers in a land that is not our own, looking forward to living in our home land (Hebrews 11:9–10).