1. Separation by nature.
By taking human nature into His Divine Person, the Word (Logos) has bridged the separation between the Creator and our created human nature. The distinction between human nature and the Nature of God remains, and that is essential to the Mystery. The Divine Nature of the Word and the human nature of Jesus of Nazareth remain distinct, and yet both are fully present in one and the same Person. He is God the Son, and He is the Son of Man.
2. Separation by sin (Here the word "reconcile" apples directly)
This is where the crucial word "propitiation" comes in, as does the word "atonement." On the cross our Lord offered up Himself as the one true sacrifice for all human sin. We say it well in our Holy Communion, with words that summarize a major theme of the Epistle to the Hebrews: "Almighty God, our heavenly Father, who of thy tender mercy didst give thine only Son Jesus Christ to suffer death upon the Cross for our redemption; who made there (by his one oblation of himself once offered) a full, perfect, and sufficient sacrifice, oblation, and satisfaction, for the sins of the whole world..." He paid it all, as the word teleo ("It is finished" John 19:30) so clearly means.
3. Separation by death
In His resurrection on the first Easter Day, our Lord defeated, triumphed over and destroyed death. The full fruit of this victory He will share with us on the Last Day when He comes again in glory (I Cor. 15). He will give us immortality, making us partakers of the eternal and unending life of the Divine Nature (II Pet. 1:4).
Perhaps the value of the word "reconcile," as Article II uses it, becomes more clear in this threefold summary.