"He came and preached peace to you who were far away and peace to those who were near." NIV translation
Paul reminds the Ephesians, and us as well, that Jesus shared His message with both Jews and Gentiles. He went into the temple and shared the news as well as meeting with Gentiles on the way. The message was the same no matter who He spoke to and always pointed the way to the Father and how everyone could have peace with God.
"For through him we both have access to the Father by one Spirit." NIV translation
Both Jews and Gentiles can become children of God. As children of God, we have the same access to the Father. That access is through the gift of the Holy Spirit which is our Counselor and Comforter.
"Consequently, you are no longer foreigners and aliens, but fellow citizens with God's people and members of God's household," NIV translation
Since there is only one God, then, we are all His and members of the same house (family). Jews and Gentiles alike are a part of that same family as we all come into His house in the same way.
"built on the foundation of the apostles and prophets, with Christ Jesus himself as the chief cornerstone." NIV translation
Every house has some type of foundation which supports the weight of the rest of the home. Here, we are told that the House of God is built on the apostles, prophets, and Jesus. The thing that all of them have in common is that they all proclaimed the Word of God which always pointed to the Chief Cornerstone which is Jesus.
"In him the whole building is joined together and rises to become a holy temple in the Lord. And in him you too are being built together to become a dwelling in which God lives by his Spirit." NIV translation
Through Jesus, all believers are joined together to form the temple called the Body of Christ. Individually, we each are also a dwelling where God lives through the Holy Spirit. There can be so much comfort in the fact that God is with you and inside you through His Spirit. The question that you must ask yourself is: Got the Spirit? If you do, then you are a temple and a part of the complete temple of God here on earth.