Question: "What exactly is a 'holy kiss'?"
Answer: There are four places in the New Testament that refer to the “holy kiss”—Romans 16:16; 1 Corinthians 16:20; 2 Corinthians 13:12; and 1 Thessalonians 5:26. In each instance, the Greek words denote a kiss which is sacred—physically pure and morally blameless. It was a common custom in most nations for people to kiss each other at meeting or parting to display their love, sincere affection, and friendship for each other. The kiss is called "holy" to distinguish it from a sexual one and from a hypocritical and deceitful one, such as Joab gave to Amasa (2 Samuel 20:9) or such as Judas gave to Jesus when he cried, “Hail Rabbi,” and betrayed Him into the hands of His enemies (Matthew 26:49).
In New Testament times, the holy kiss was a sign of greeting, much like the modern handshake. For Christians, it further expressed brotherly love and unity. The holy kiss was especially precious to the new believers during the early church years, because they were often outcasts from their own families because of their new faith. These new believers gloried in the new spiritual kinship they had found among other Christians. Furthermore, the holy kiss from a Jewish Christian to a Gentile believer was evidence that the Gentiles were accepted fully into Christian fellowship, despite the teachings of the Judaizers, those who would return to the Mosaic law as their source of justification. So prominent were these false teachers in the early church that they even temporarily drew such a prominent Christian as Peter into their web of deceit (Galatians 2:11-13). The holy kiss between the Jewish and Gentile believers was done righteously in recognition that all believers are brothers and sisters in the family of God.
Whether or not the holy kiss should be a tradition we carry on today is not clear in Scripture. Whether or not our salutations to our brothers and sisters in Christ include the holy kiss, the important thing is that our greetings spring from real love and friendship, be characterized by sincerity, and represent true Christian fellowship.