כי איל מלואים הוא, this was the reason that the right thigh was burned on the altar. This practice did not apply to any of the other animal sacrifices. [with the exception of burnt-offerings which were burned up completely. Ed.] The Torah views the right thigh of the animal as equivalent to the right hand of a human being. Wherever in the Torah the word אצבע appears in the same context as the priesthood, the reference is to the finger of the right hand. (Menachot 10).

והנפת, this “waving” applies to the part of the sacrificial animal that the priests are given to eat. The main reason is that the priest should remain aware that he eats from שלחן גבוה, “from G’d’s table,” so to speak, i.e. that his portions are a “kick back,” totally voluntary gift from G’d, and that he does not eat by “rights,” i.e. that this is what the owner of the sacrificial animal designated for him. In this instance, also the part of the animal which would normally be his to eat wound up on the altar instead of being consumed by the priests, it being an introductory symbolic procedure. [perhaps similar to the concept of ראשית, the “first” part of crops which need to be consecrated to G’d of produce originating from the earth. Ed.]

ולמלא בם את ידיהם, “with which to become inaugurated.” Subsequent generations of the priests did not need to undergo these procedures seeing they had been born as priests, their status being hereditary, as opposed to Aaron and his sons.

ושכנתי בתוך בני ישראל. There to receive their service with goodwill and in order to listen to their prayers.

והייתי להם לאלוקים, and I will supervise their affairs without resorting to an intermediary. They will have no reason to be afraid of what astrology portends, seeing that they (the Jewish people) are far more honoured by Me than are the celestial planets, etc. The very fact that I guide others’ fate only by means of agents, intermediaries, testifies to the eternal existence of the Jewish people.