When Jesus taught his disciples to pray he told them to pray to their Father in heaven and ask "Thy Kingdom come and Thy will be done on earth as it is in heaven."
Again Jesus told Nathaniel that he would see angles ascending and descending on the Son of Man (John 1:51). This was an allusion to Jacob's dream in Genesis 28:12 where Jacob saw a ladder connecting heaven and earth with angles ascending and descending upon it.
Jesus is the connection between heaven and earth. The incarnation does not teach us that we are to be like Jesus in order that we can one day go to heaven. No. The incarnation teaches that God is so fundamentally set on saving this world that he has sent His Son to begin a mighty restoration process. A good way to understand this is by looking at Jesus' ministry, and the miraculous ministry of the Apostles in Acts, as an embodiment of what he taught his disciples to pray: Thy Kingdom come on earth as it is in heaven.
In John 14 Jesus addresses his disciples about how he will not really leave them when he goes to his Father. He says "I will come to you." (John 14:18) Jesus is talking about his presence with the disciples by his Spirit; the Holy Spirit. Put in conjunction with what I wrote above we can see that this idea of heaven being on earth did not end when Jesus ascended to the right hand of the father. The connection between heaven and earth is still vital because of the Holy Spirit.
However, we must be careful and not over-individualize this concept with our Modern lenses. Our natural tendency would be to approach this teaching about the Holy Spirit as though each Christian has their own individual connection to heaven through the indwelling of the Holy Spirit. Though it is true that the Holy Spirit does indeed indwell believers and we do have access to the throne of grace (Hebrews 4:16) these blessings are always connected to the wider context of Christian community.
We can gain a better understanding of this from two places in Paul's writings. Firstly, we must remember that Paul brings up the metaphor of the church and a body (1 Corinthians 12:12-27). Paul reminds the Corinthian believers that each member is connected to the body. This means that we do not participate in the Holy Spirit in isolation, we experience it in community. In fact the church is the community of the Spirit.
Secondly, we can gain a great understanding of how Paul sees the Spirit indwelt church as the connection between heaven and earth in his letter to the Philippians, particularly chapter 3. In Philippians 3:20 Paul says "But our citizenship is in heaven and from it we await a savior, the Lord Jesus Christ." Many people have taken this passage to mean Just the opposite of what it is actually saying. A common understanding of it is that because our citizenship is in heaven we must wait out our alien existence here on earth till our death or the second coming of Christ when we will go to heaven. This is a woeful misunderstanding which carries dire consequences.
The city of Philippi was a colony of Rome in Greece. In fact, much of the city was populated by Roman ex-patriots. This meant that while they lived in Philippi they were "technically" citizens of Rome. Because they were citizens of Rome it was their objective to (more or less) "Romanize" the city they were living in. Being a citizen of Rome carried such weight to these Roman ex-patriots that they saw it as their "Roman duty" to transform the preexisting Greek culture of Philippi into a Roman culture.
Paul used his language carefully when he told the Philippian Christians that they were citizens of heaven. What Paul was doing was telling them that, just as those Roman ex-patriots who live in Philippi see it as their goal to "Romanize" the city, so too are you called to "heavenize" the city of Philippi because you are "citizens of heaven." Peter Leithart makes this point very well in his book Against Christianity:
Paul was mounting a polemic against the imperial ideology, affirming that Jesus, not Caesar, is "Lord" and "Savior," both prominent terms in imperial propaganda. Paul's claim that Christians are citizens of a heavenly politeuma [polity/city] further indicates that the Philippian Christians are to consider themselves a colony of heaven more than as a colony of Rome. Paul imitated Christ by giving up his privileges as a Hebrew of the Hebrews [Philippians 2], and he exhorted the Philippians to follow his example by treating their Roman citizenship and attachment to the Romans emperor as "rubbish" for the sake of Christ and His heavenly politeuma.
In short: throughout Philippians, which some identify as one of the least political of Paul's letters, Paul was treating the Church as an alternative to the politico-religious organization of the city and of the empire. (Pg. 31)
The church cannot afford to sit back and assume that their heavenly citizenship opts them out of reforming/heavenizing the world around them. Because the church truly is the Body of Christ indwelt by the Spirit this means that the church, like its Lord, is the connection between heaven and earth and angels ascend and descend upon her. The church is "a colony of heaven" on earth. Leithart, again, puts it well in saying:
Churches on earth are outposts of the heavenly Jerusalem, anticipations of the final city, joined in a mysterious way, especially in liturgy, with the heavenly city. Every Lord's Day, we, like John [Revelation 4], enter into heavenly places, even while we remain in the middle of the earthly assembly. Heaven is in our midst, and we are in the midst of heaven. Responding with homage and worship to the authority of the risen and ascended Lord, the Church is formed as a polity. (pg. 25)
Doug Wilson put it succinctly when he said somewhere "the church has a retractable roof."
Food for thought.