The verse "This greeting is by me, Paul, with my own hand" (1 Corinthians 16:21) is generally understood to mean that Paul personally wrote this concluding greeting. Here's a breakdown of why and what that signifies:

Authentication: In ancient times, letter writing was often done by scribes (professional writers). Paul likely dictated most of his letters to a scribe like Tertius (Romans 16:22). By adding this final greeting in his own handwriting, Paul was authenticating the letter as truly coming from him. It served as a kind of signature, proving that the entire letter hadn't been altered or forged.

Personal Touch: Beyond just authentication, it likely added a personal touch. It was a way for Paul to connect with the Corinthian church in a more direct, tangible way. He's saying, "Yes, a scribe wrote most of this, but this part, the part where I send my love and greetings, is my handwriting. I'm thinking of you personally."

Warning Against Forgery: Some scholars also suggest it might have been a warning against false letters circulating in Paul's name. By pointing out that he always included a handwritten greeting, recipients could be wary of letters claiming to be from Paul that lacked this feature. Paul warns of such forgeries in other places (e.g., 2 Thessalonians 2:2).

In short, the verse highlights the authenticity of the letter, adds a personal element to the communication, and potentially serves as a safeguard against forgeries.