embrace, greet, salute, take leave

Boyd’s Bible Dictionary:

(good health, greeting). Personal salutation very formal in East. The “peace be with thee,” or similar expression, was accompanied by a profound bow, kiss, embrace, or other courtesy (Gen. 19:1; 1 Sam. 25:23; Matt. 10:12; Luke 1:41). Epistolary salutation took the form found in the opening and closing of the epistles (Rom. 1:7; 1 Cor. 1:3).

Concise Bible Dictionary:

The brotherly greetings expressed at the close of nearly all the epistles. They were sent from the saints located where the epistles were written to the saints addressed, together with, at times, the injunction to greet one another with “a holy kiss,” that being the ordinary form of salutation in the East among the men as well as among the women (Rom. 16:5-23; 1 Thess. 5:26; Titus 3:15).
When evil doctrine had spread in the professing church, the question of salutation became serious. The “lady” to whom the apostle John wrote was strictly enjoined not to receive into her house anyone who brought not good doctrine, nor was she even to salute such a one; for to do so, would be to become morally a partaker of his evil deeds (2 John 1:10-11; compare Rom. 16:17).
Salutations in the East being often very lengthy and of mere ceremony, may well account for those sent in haste being told to salute no one by the way (2 Kings 4:29; Luke 10:4).

Strong’s Dictionary of Greek Words:

Greek:
ἀσπάζομαι
Transliteration:
aspazomai
Phonic:
as-pad’-zom-ahee
Meaning:
from 1 (as a particle of union) and a presumed form of 4685; to enfold in the arms, i.e. (by implication) to salute, (figuratively) to welcome
KJV Usage:
embrace, greet, salute, take leave