The inauguration of the priests involved a unique sacrifice that blended the characteristics of a completely burnt offering and a peace offering. During this ceremony, the choicest parts of the ram were separated and dedicated to the altar. The primary component was the fat, though its exact identification is debated. Some identify it as the fat covering the intestines or stomach, linking it to legal definitions of forbidden fat as either a thin, peelable membrane or a broader, dress-like layer [רש״י, גור אריה, מזרחי]. Others simply view it as the fat on the entrails [אבן עזרא, ביאור יש״ר], while another perspective suggests it refers to the fat located at the end of the tail [העמק דבר].
Along with the internal fat, the offering included the thick, fatty tail typical of most sheep [ביאור שטיינזלץ]. This portion was removed from the area of the kidneys downward. The kidneys themselves hold a special metaphorical significance as the body's advisors. This advisory role is attributed either to their physiological function of filtering toxins from the blood or to their existence as a pair, which represents the ability to weigh advice from multiple perspectives [רש״י, ברכת אשר]. Dedicating the tail is a practice exclusive to sheep and rams, never applying to bulls or goats [רש״י]. Additionally, the appendage attached to the liver was also included among the parts offered on the altar [אבן עזרא הקצר].
A striking departure from standard sacrificial rules occurred with the right thigh. Normally, the right thigh of a peace offering is given to the priest as his portion to eat. In this inauguration ceremony, however, it was burned on the altar alongside the internal organs [שד״ל, רש״י]. Commentators offer several explanations for this exception. One approach connects it to the nature of the ceremony itself: just as the right thigh represents the animal's right side, the priests perform their service and inauguration with their right hands, making it fitting to dedicate this specific part to the altar [ספורנו]. Another explanation focuses on the mixed nature of the sacrifice; because it shared aspects of a burnt offering, the finest portion of the meat was given to God [העמק דבר]. Conceptually, the thigh symbolizes strength, stability, and independence. Burning it served as a profound lesson for the newly appointed priests, teaching them that their power and material status were not meant for personal enjoyment, but were to be entirely devoted to God and the community [רש״ר הירש]. However, this specific practice was a temporary, one-time instruction for the first day of the inauguration; during the remaining days, the thigh was eaten as usual [ריב״א, חזקוני, ביאור יש״ר].
The very term for this inauguration sacrifice shares a linguistic root with concepts of wholeness and peace. It functioned as a peace offering that established harmony among all participants: the altar received the fats and the right thigh, the acting priest—which in this unique case was Moses—received the breast, and Aaron and his sons, as the owners of the sacrifice, ate the remaining meat [רש״י, מזרחי]. Despite being classified as a peace offering, which is typically eaten over two days and a night, the timeframe for consuming this specific sacrifice was restricted to a single day and night, similar to a sin offering. Because the meat was consumed exclusively by the priests rather than the general public, this strict time limit ensured it would be eaten with a hearty appetite and a sense of reverence before its flavor could fade [פרדס יוסף].