But what does it mean that Jesus was sinlesss? The first thing to note is that this concept only occurs in Hebrews (chapter 4). And the immediate context in Hebrews around that concept presents Jesus as our high priest, who has ascended into heaven with an eternal priesthood, having made purification for sins once for all.
But again, what does the sinlessness of Jesus have to do with this? It has everything to do with the quality of his sacrifice. Let me share a couple sentences from the first chapter of Leviticus.
"If the offering is a burnt offering from the herd, you are to offer a male without defect."
"If the offering is a burnt offering from the flock...you are to offer a male without defect."
Thus, part of the requirements to fulfill the sacrificial system of the law were a male without defect. That is, without blemish. That is, without the blemish of sin. So, Jesus is sinless, so that he can be our perfect high priest and a perfect sacrifice of atonement without blemish (sin).
Now we have a purpose for and a reason to read Leviticus. It is about sacrifice, purity and holiness. Who can go in before the Lord? This is the question Leviticus answers, and the answer centers around the Day of Atonement in chapter 16.
But we anticipate the greater things. "Therefore, since we have a great high priest who has ascended into heaven, Jesus the Son of God, let us hold firmly to the faith we profess."