There are many similar questions, and you will think it is a repeat unless you read the rest of the body. The magi seeking to worship a king seems strange. Even stranger is Herod's claim to want to worship that king.
Now after Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, wise men from the east came to Jerusalem, 2 saying, “Where is he who has been born king of the Jews? For we saw his star when it rose and have come to worship him.” (Matt. 2:1–2, ESV)
Then Herod summoned the wise men secretly and ascertained from them what time the star had appeared. 8 And he sent them to Bethlehem, saying, “Go and search diligently for the child, and when you have found him, bring me word, that I too may come and worship him.” (Matt. 2:7–8, ESV)
The German university professor, Heinrich Greeven, wrote the article for this word in TDNT, put together by Gerhard Kittel using top German scholarship. Dr. Greeven here disagreed with the answers previously given at this site.
Greeven, Heinrich. (1964–). "προσκυνέω, προσκυνητής." G. Kittel, G. W. Bromiley, & G. Friedrich (Eds.), Theological dictionary of the New Testament (electronic ed., Vol. 6, p. 758-764). Grand Rapids, MI: Eerdmans.
Septuagint (LXX)
The Septuagint. In the LXX προσκυνεῖν is virtually the only rendering of הִשְׁתַּחֲוָה on the one side and סָגַד24 or סָגֵד (Aram.)25 on the other; both words have the basic sense “to bow.” It is also used once each for נָשַׁק “to kiss,” עָבַד “to serve,” “to worship” Ps. 97:7, זוּעַ (Aram.)27 “to tremble,” and in 3 instances it is equivalent to כָּרַע (“to bow”) with הִשְׁתַּחֲוָה, Est. 3:2 (twice), 5. προσκυνεῖν naturally suggested itself for חִשְׁתַּחֲוָה, since the Heb. word, originally denoting only a movement of the body, had become a cultic tt. The further definitions which often accompany it, e.g., “to the earth”28 or “to do obeisance,” leave us in no doubt as to the meaning.30 It makes no odds whether the proskynesis is to God or the gods or to men. That προσκυνεῖν can be used for (→ n. 26) or par. to נָשַׁק (Ex. 18:7) shows that the element of kissing, including cultic kissing, was still present in the Gk. word at the time of the LXX.
Almost three-quarters of the instances of προσκυνεῖν in the LXX relate to veneration and worship of the true God and Lord or to that of false gods.... -- Greeven, Vol. 6, p. 760-761.
New Testament
Dr. Greeven references every occurrence of προσκυνέω in the New Testament. Based on its use in the New Testament, he sees προσκυνέω differently.
- When the NT uses προσκυνεῖν, the object is always something—truly or supposedly—divine. Mt. 18:26: πεσὼν … προσεκύνει αὐτῷ (v. 29: πεσὼν … παρεκάλει [different word] αὐτόν) is an exception only in appearance, for Mt. can hardly be using these words for the proskynesis of a slave to his master or to the king, → 163, 16. This is refuted not only by the use of προσκυνεῖν elsewhere in the NT but especially by the fact that Mt. has altered or expanded his Marcan original in no less than five passages in order to describe the gesture of those who approach Jesus explicitly as proskynesis: the leper in Mt. 8:2 cf. Mk. 1:40; Jairus in Mt. 9:18 cf. Mk. 5:22; His companions in the boat, Mt. 14:33 cf. Mk. 6:51; the woman of Canaan, Mt. 15:25 cf. Mk. 7:25; the mother of James and John, Mt. 20:20 cf. Mk. 10:35. The only instance to the contrary seems to point in the same direction, for it is very probable that Mt. 27:29 cut out the proskynesis of the soldiers (Mk. 15:19) because elsewhere the word always expresses true adoration for Mt. As regards Mt. 18:26 it may thus be concluded that the parable is not pure in Jülicher’s sense but gives us a glimpse of God Himself behind the ἄνθρωπος βασιλεύς. -- Greeven, Vol. 6, p. 763.
- The conversation of Jesus with the Samaritan woman in Jn. 4:20–24 leaves an initial impression that προσκυνεῖν is used here in a wholly figurative sense, since Jesus speaks of προσκυνεῖν in spirit and in truth. But if prostrating oneself no longer plays any definite role, the reference in the statement and answer is to the place of worship. Furthermore, there obviously stands in the background the technical use of the word for the pilgrimage of Jews to Jerusalem, so also Jn. 12:20; Ac. 8:27; 24:11. If instead of naming a place to which the pilgrims should go to worship Jesus says that the true place of worship is in the spirit and in truth this is an oxymoron. Undiluted προσκυνεῖν, the act of worship which is concrete in place and gesture, is lifted up to a new dimension: “spirit and truth.” -- Greeven, Vol. 6, p. 764.
This is only an introduction to Dr. Greeven's article.
I'm hoping for answers taking Dr. Greeven's article into account; not necessarily agreeing with it.
Supplemental
When Peter entered, Cornelius met him and fell down at his feet and worshiped [προσεκύνησεν] him. 26 But Peter lifted him up, saying, “Stand up; I too am a man.” (Acts 10:25–26, ESV)
Peter rejects the proskynesis of Cornelius with the words: “I too am a man,” Ac. 10:25 f. -- Greeven, Vol. 6, p. 764.