Here in Hebrews 13:12-16, Paul is outlining the proper order of sacrifice in our life, which is interesting in that it is slightly different from the initial order given in Leviticus of the burnt, grain, peace, sin, and trespass offerings. Why is that? Well, the order here in Hebrews 13 is the same found in Leviticus 9, which records the first observance of the Aaronic priesthood.
In both Leviticus 9 and in Hebrews 13:12, we see that first comes God's sacrifice. The sin and trespass offering has to come first to open a door and enable our relationship with God. We could never approach God as a whole burnt offering in complete devotion to God until Jesus Christ's sin offering suffered outside the gate, opened the door to our relationship with God. That had to come first.
And once that happens, our response of sacrifices and repentance and devotion to God found in Hebrews 13:15 represent the burnt offering, our complete devotion and obedience to God. That comes next and results in God with His enabling Spirit to come right into our very temple, our body. We can jot down I Corinthians 6:19-20. And then right on top, just like the burnt offering and a meal offering happened always together, right on top, enabled by His Spirit, is Hebrews 13:16, our sacrifices and service to man representing the grain offering.
The result is seen in the peace offering of unity and peace in our relationship with God the Father, Jesus Christ, and Their extended Family, the Body of Christ. And these sacrifices on God's table symbolize a complete meal that is indeed a sweet-smelling aroma to God.