Hebrews 8:3-5 meaning

Every Levitical high priest offered both gifts and sacrifices (v 3) before the Lord; it was a requirement of the job. Therefore, it would stand to reason that Jesus, our High Priest, would have something to offer. The Pauline Author writes: So it is necessary that this high priest also have something to offer (v 3). 

Jesus was sent to fulfill a far greater purpose; He did not offer up the same sacrifices and gift offerings that the Levite priests offered. Those priests made sacrifices that had to be repeated (sometimes daily, 2 Chronicles 8:13) in order to atone for sins and make peace with a holy God, but they first had to atone for their own sins. 

However, if Jesus were on earth, He would not be a priest at all, since there are those who offer the gifts according to the Law (v 4). He would not have met the qualifications of priesthood.

The Pauline Author is establishing that the things of earth are shadows of heaven and that Christ bypasses limitations of earthly priests and tabernacles. He is showing the evidence for the obvious and implied reality that Jesus's sacrifice was once, for all. It is a perfect sacrifice that completely fulfilled and "finished" the necessary work of atoning for sins, and therefore does not have to be repeated.

When Moses was about to erect the tabernacle, he was warned by God, who said, "See that you make all things according to the pattern which was shown you on the mountain" (v 5) (Exodus 25:40). Prior to building the tabernacle, God had given Moses a glimpse of the original to model it after. All earthly priests have only served as a model, a copy and shadow of the heavenly things (v 5). 

Jesus is a better high priest, because He is the real thing, not a replica. And He is in heaven right now doing His high priestly job, mediating our relationship with God, as the following verses explain.