Charles Ellicott Commentary Exodus 18:7

"And Moses went out to meet his father-in-law, and did obeisance, and kissed him: and they asked each other of their welfare; and they came into the tent." — Exodus 18:7 (ASV)

Moses went out ... And did obeisance. —Eastern etiquette required going out to meet an honored guest (Genesis 18:2; Genesis 19:1, and so on). This obeisance was entirely voluntary and marks the humility of Moses, who, now that he was the prince of his nation, might well have required Jethro to bow down to him.

And kissed him. —Kissing is a common form of greeting in the East, even between persons who are in no way related. Herodotus says of the Persians: “When they meet each other in the streets, you may know if the persons meeting are of equal rank by the following token: if they are, instead of speaking they kiss each other on the lips. In the case where one is a little inferior to the other, the kiss is given on the cheek” (Book i. 134). (Compare 2 Samuel 15:5; 2 Samuel 19:39; 2 Samuel 20:9; Matthew 26:48–49; Acts 20:37, and so on; and for the continuation of the custom to the present day, see the collection of instances given in the article Kiss, in Smith’s Dictionary of the Bible, vol. ii., p. 46.)

They asked each other of their welfare. —Hebrew, wished peace to each other —exchanged, that is, the customary greeting, “Peace be with you.”