(1) On the eighth day Moshe called Aharon and his sons, and the elders of Israel. (2) He said to Aharon: “Take yourself a calf of the herd for a sin offering and a ram for a burnt offering, without blemish, and bring them before the Eternal. (3) And speak to the Israelites, saying: Take a goat for a sin offering; a calf and a lamb, yearlings without blemish, for a burnt offering; (4) and an ox and a ram for an offering of well-being to sacrifice before the Eternal; and a meal offering with oil mixed in. For today the Eternal will appear to you.” (5) They brought to the front of the Tent of Meeting the things that Moshe had commanded, and the community leadership came forward and stood before the Eternal. (6) Moshe said: “This is what the Eternal has commanded that you do, that the Presence of the Eternal may appear to you.” (7) Then Moshe said to Aharon: “Come close to the altar and sacrifice your sin offering and your burnt offering, making expiation for yourself and for the people; and sacrifice the people’s offering and make expiation for them, as the Eternal has commanded.”(8) So Aharon came close to the altar and slaughtered his calf of sin offering. (9) Aaron’s sons brought the blood to him; he dipped his finger in the blood and put it on the horns of the altar; and he poured out the rest of the blood at the base of the altar.

Take yourself a calf - To let him know the Holy Blessed One would grant him atonement by means of this calf for the incident of the golden calf which he had made (Midrash Tanhuma, Shemini 4)

Come close to the altar... and Aharon came close to the altar and slew the calf -

In my opinion, the simplest explanation is that he was saying, ‘Come close to the north side of the altar and sacrifice the offerings.’ Because they would do the sacrifices on the north side. But Moshe said it in a shorthand, because Aharon already knew that.

In Torat Kohanim [the standard midrash on Leviticus], our rabbis took note of this problem, and they gave a parable. What is this like? Like a king who marries a woman, but she is too shy to be with him. So her sister comes in and says to her, “Why did you enter into this arrangement, if not to sleep with the king? Rouse yourself and go in and sleep with him!” So did Moshe say to Aharon, “My brother, why were you chosen to be the high priest, if not to serve God? Rouse yourself and go perform your service!”

But some say that Aharon saw the altar take the form of a bull, and he was afraid of it! So Moshe went over to him and said, “Aharon, my brother, rouse yourself and go up close to it.” And that is why it says “Come close to the altar,” and then, “He went close to the altar,” with zeal.

The reason for [this vision] is that Aharon was a holy man, dedicated to God. His soul was completely free of sin - except for the sin of the Golden Calf. So this one sin was constantly in his thoughts. As Psalm 51 says, “My sin is before me, always.” So it appeared to him that the form of a calf was there, blocking his atonement. And that is why Moses said to him, ‘Rouse yourself, you should not be so self-punishing! God wants your service!’

Others explain that it was the Satan who showed him this apparition, just as they have said there (in Torat Kohanim, Shemini 3) “My brother Aharon, although God has agreed to grant atonement for your sin, you must nonetheless close the mouth of Satan [through your offerings], lest he accuse you when you enter the Sanctuary etc.”

And this is the reason it says [at the end of the verse], “and atone for yourself and for the people…” [Moses] was telling [Aaron], “Come close to the altar” to offer all the sacrifices, but first do your own sin offering and burnt offering, and atone for yourself first with your own sacrifices. And then, afterwards, you will perform the offering for the people, and atone for them with their sacrifice. Moses was teaching Aaron that one must become innocent in order to atone for the guilty. (Yoma 43 b.)