Exodus 29:36-37 meaning

Verse 35 stated that the ordination of the priests was a ceremony lasting seven days. Verses 36 - 37 describe how the altar was to be set apart during that time. The LORD commanded that each day (for seven days) you shall offer a bull as a sin offering for atonement, which resulted in the purification of the altar.

The sin offering was the atonement, the price paid for purifying the altar. God commanded that Moses shall anoint it (the altar) to consecrate it, setting it aside for a special purpose. Here, it would be set aside to be the place where offerings were given to the LORD. The idea seems to be that the new high priest does not change the basic function of the ceremonies and what they represent. They are to continue as commanded notwithstanding a new leader.

Verse 37 is a restatement of the length of the ordination ceremony. It was to last for seven days, during which they would make atonement for the altar and consecrate it. The altar needed purification so it would be most holy and whatever touches the altar (such as the sacrificial animals offered on it) shall be holy.