Then from the sacrifice of the peace offering he shall offer as a food offering to the Lord its fat; he shall remove the whole fat tail, cut off close to the backbone, and the fat that covers the entrails and all the fat that is on the entrails and the two kidneys with the fat that is on them at the loins and the long lobe of the liver that he shall remove with the kidneys. And the priest shall burn it on the altar as a food offering to the Lord.” (Leviticus 3:9–11, ESV)

Here is a good example of why Leviticus drags on for so many modern readers.  The instructions for a food offering from the sacrifice of the peace offering go on and on talking about fat, entrails, kidneys, the lobe of the liver, etc.  It is so far removed from our own experience that we can barely make it through a chapter before our mind begins to wander.

Contrast this with the experience of the Israelites.  Leviticus was the first book of the Torah which they taught their children.  Why?  They taught it because Leviticus instructs them how to live in the presence of a holy God.  What could be more important than that?

Why the obsession with fat in so many of the sacrifices?  Gordon Wenham comments:

Calvin may well be right in thinking that fat was thought of as specially belonging to God. Certainly fat in the OT can be synonymous with “the best” (Gen. 45:18; Ps. 81:17 [Eng. 16]). By giving the fat the worshiper was giving the best of the animal; and insofar as the animal was thought to represent the man, the worshiper showed he was giving God the best part of his life.

The New Testament believer has a connection with the Israelites, but rather than sacrifice an animal, now we are instructed to make our whole life a living sacrifice; we are called to offer up a sacrifice of praise; and Hebrews instructs us

Through him then let us continually offer up a sacrifice of praise to God, that is, the fruit of lips that acknowledge his name.” (Hebrews 13:15, ESV)

We cannot understand these New Testament commands without understanding Leviticus.  This is why the book is so important.