It means that the Spirit has come to us, regenerating our hearts and minds to that of Christ, giving new life to us, bringing us into the fellowship of the Son and the Father, and making us heirs of resurrection and immortality.
St. Paul the Apostle writes in Romans ch. 8, "If the Spirit of Him who raised Christ from the dead dwells also in you, He who raised Christ from the dead will also give life to your mortal bodies through the Spirit who dwells in you."
The Spirit of the Father, who proceeds from the Father, who is also the Spirit of the Son (and therefore Bond between Father and Son) is sent to dwell in Christ's Faithful, in His Church; received in the waters of Holy Baptism by the promise and word of God, we are united to Jesus Christ Himself, made members of His Body by our being mystically united to His death and resurrection and receiving His Body and Blood at His Table we find ourselves partakers and sharers in the Life of God, intimates of the Holy Trinity. And if united to Christ, in God, through the unity and power of the Spirit, we are heirs of God, joint-heirs with Christ, and thus recipients of all the good things of Christ: Heirs of the resurrection of the dead, of life-everlasting and immortality, of a new life borne out of new creation of God wrought through Christ Jesus whereby there is reconciliation, peace, justice, and life. Age to Come, world without end, beginning here and now as the kingdom comes and is coming. Inaugurated by He who bore Crown and Cross and consummated at the Parousia, the glorious appearing and coming of our God and Savior, Jesus Christ, world without end.
-CrypoLutheran