The main understanding in the New Testament is “obeisance”. (see Thayer)
It can also mean worship when directed to Jehovah.
G4352 προσκυνέω proskuneō Thayer Definition:
1) to kiss the hand to (towards) one, in token of reverence
2) among the Orientals, especially the Persians, to fall upon the knees and touch the ground with the forehead as an expression of profound reverence
3) in the NT by kneeling or prostration to do homage (to one) or make obeisance, whether in order to express respect or to make supplication
3a) used of homage shown to men and beings of superior rank
3a1) to the Jewish high priests 3a2) to God 3a3) to Christ 3a4) to heavenly beings 3a5) to demons
[Compare definition 3a1) to Hebrew 3:1]
In 1611 when the KJV was translated, the word “worship” reflected Proskuneō perfectly, basically meaning “to bow down” and was directed to men and God. (See “Truth in Translation” page 29)
The word “Worship” in the Noah Webster's 1828 Dictionary of American English is not limited to the narrow understanding people apply to it today. (As compared to my 1985 The American heritage Dictionary)
In all usages of the word ‘worship’ in 1611 & 1828, you had to choose one of its two basic definitions –
1) That to do with ‘civil honor’ (see * above) (Matt 18:26 KJV & Rev 3:9 KJV)
2) The religious honor to be directed solely to Jehovah. (Matt 4:10)
According to the book “Truth in Translation” by Jason BeDuhn:
“When the word [Proskuneō] is used to refer to the actions of [non-believers] most translations stick to the literal meaning of kneeling or bowing. But when the disciples of Jesus are the actors, suddenly we see “worship” everywhere.”
“In the cultural context of the events, the gesture [to bow down] makes perfect sense. In the ancient world, one bows to power. Most translation choose to import the modern meaning of “worship” into the passage(s) because of the recognition by the disciples that they are in the presence of “a son of God.” This title was used of someone especially chosen and protected by God, and bestowed with power by him – especially a king. The idea was used of Solomon (2 Sam. 7:14) . . . By misreading the words used of Jesus by the disciples, by wrongly making them in light of the Christian doctrine about Jesus’ divinity as “the Son of God”, most translations add to the text the false idea that the disciples are depicted worshiping Jesus, when in fact, . . . they are reacting to his evident powers with awe.” (Also see Acts 2:22)
This creates a circular reasoning. “I believe Jesus is God, so to bow down to him must be worship, thus translating [Proskuneō] ‘bow down’ as worship. Then reading that people worshiped Jesus proves to us that Jesus is God. So bow down must be worship, worship must mean Jesus is God . . . (on and on and on)”
When Modern Bibles translate this word as ‘worship’ when applied to Jesus, this is based on the ‘interpretation’, of the trinity, not according to historical and scriptural context.
Thus the honest or ‘unbiased’ translation of Proskuneō in today’s English, when applied to Jesus is ‘obeisance’ the basic meaning of the word and not ‘worship’. ~ “most translations add to the text the false idea that the disciples are depicted worshiping Jesus,”