"'"If you offer an animal from the flock as a fellowship offering to the Lord, you are to offer a male or female without defect. If you offer a lamb, you are to present it before the Lord, lay your hand on its head and slaughter it in front of the tent of meeting. Then Aaron's sons shall splash its blood against the sides of the altar. From the fellowship offering you are to bring a food offering to the Lord: its fat, the entire fat tail cut off close to the backbone, the internal organs and all of the fat that is connected to them, both kidneys with the fat on them near the loins, and the long lobe of the liver, which you will remove with the kidneys. The priest shall burn them on the altar as a food offering presented to the Lord."'" NIV translation
The regulations for offering a lamb took into the account the fact that there was a specific kind of sheep that had a tail that contained a bunch of fat. Fat represented the best of an offering because it was a sign that an animal was well taken care of (it ate well). It is a reminder that we are always to present our best to the Lord.