Use it when some things have been said about someone or something, but a relevant fact or opinion was left out. Some equivalents: I forgot to mention that... You should also know that...

The interesting word is "might". If you take away that word the meaning does not really change: "He's a good person, I add". ("I add" = "in addition") That is a good matter of fact sentence, but a boring one. Adding "might" endows this matter of fact sentence with an aura of certainty, daring, possibility, or creativity. Who knows? The possibilities are endless. And, do not forget that "might" and "might not" mean the same thing! How can that be? If you might, then you might not. If you might not, then you might! What mystery! See how much more interesting it becomes by adding that one simple word?

It adds information that the speaker feels is important but in a way that is different from that being discussed. My daughter and her boyfriend are in love and I’m happy they are planning to get married! He makes a great living I might add. (That’s one of the reasons I’m happy but it’s not the socially acceptable one to talk about) A: So you think that conversing with native speakers is an effective way to learn a language because it practices hearing and speaking the language in a relaxed setting? B: Yes. And it’s fun I might add! (It’s relevant to success, but not for the reasons initially given)

adding one's own opinion to a synopsis.