Could someone explain what is meant the this part of the Scripture: “…to offer spiritual sacrifices acceptable to God through Jesus Christ”?
spiritual sacrifice: see Psalm 51. The entire psalm is relevant, but v. 18-19 in particular touches on spiritual sacrifice:
For you do not desire sacrifice or I would give it;
a burnt offering you would not accept.
My sacrifice, O God, is a contrite spirit;
a contrite, humbled heart, O God, you will not scorn.
acceptable to God: see Leviticus 22:17-30. Sacrificial animals should be unblemished (and free of injury or deformity). So we should strive to cleanse our spirit of evil and disorder, that it may be an acceptable offering.
through Jesus Christ: Our sacrifices are not acceptable on our own merits. Our spirit is never perfectly free of blemish or disorder. Our imperfect prayers and our imperfect hearts are purified and made acceptable through the intercession of Jesus Christ. See Hebrews 10, especially v. 19-23:
Therefore, brothers, since through the blood of Jesus we have confidence of entrance into the sanctuary by the new and living way he opened for us through the veil, that is, his flesh, and since we have “a great priest over the house of God,” let us approach with a sincere heart and in absolute trust, with our hearts sprinkled clean from an evil conscience and our bodies washed in pure water. Let us hold unwaveringly to our confession that gives us hope, for he who made the promise is trustworthy.
Paul goes on to say, in v. 24-25:
We must consider how to rouse one another to love and good works. We should not stay away from our assembly, as is the custom of some, but encourage one another, and this all the more as you see the day drawing near.
Our sacrifice is not just to benefit ourselves. The priest offers a sacrifice on behalf of his people. Paul reminds us here to build faith and love in our brothers and sisters. There may be better citations on this point, but I have to hurry off now!