Martin Lloyd-Jones in his Exposition of Ephesians 2 says:
There are two ways of looking at this great statement [union with Christ]. There are some people who take a purely objective view of it. They think of it exclusively in terms of our position, or our standing, in the presence of God. What I mean is that they think of it as being something that, in a sense, is already true of us in Christ, but is not true of us in practice. […] They say that it is true of us by faith now, but actually only by faith. It is not real in us now: it is entirely in Him. But it will be made real in us in the future. Now that is what I call the purely objective view of this statement. And of course as a statement, it is perfectly true, except that it does not go far enough.
This is the way I’ve always envisioned it. Union with Christ is not only our position in Christ. It’s something that changes us, feeds us, something we meditate on, something that hopefully affects how we act as we live in union with him. If two people are married, there is usually a relationship that goes on because of it, not just a legal document that was enacted at a ceremony. It should also impel us to act in a godly manner, because he is in us and we are in him. (Acts 17:28, Ephesians 2:22, Colossians 2:6-7)
But if anyone obeys his word, God’s love is truly made complete in him. This is how we know we are in him: Whoever claims to live in him must walk as Jesus did.
1 John 2:5-6
Later he continues:
“I am the vine, ye are the branches” (John 15:5). The union between the branches and the vine is not mechanical: it is vital and organic. They are bound together: the same sap, the same life is in the stock as in the branches. But that is not the only illustration used. At the end of the first chapter of Ephesians, Paul says that the union between a Christian and the Lord Jesus Christ is comparable to the union of the various parts of the body with the whole body, and especially with the head. […]
All these blessings that we enjoy become ours because we are joined to Christ in this double manner: in the forensic, federal, covenant manner, but also in this vital and living manner. We can therefore claim that what has happened to Christ has happened to us. This is the marvel and mystery of our salvation, and it is the most glorious thing we can ever contemplate! The Son of God, the Second Person in the eternal Godhead, came down from heaven to earth; He took unto Him human nature, He joined human nature unto Himself, He shared human nature; and as the result of His work we human beings share His life and are in Him, and are participators in all the benefits that come from Him.
In another excellent article, Michael Horton writes:
Regeneration, or the new birth, is the commencement of this union. God brings this connection and baptism even before there is any sign of life–“while you were dead…he made you alive” (Eph.2:1). […] Through union with Christ, we receive his righteousness imputed (justification) as well as his righteousness imparted (sanctification).