If you're a company with an established brand, you've likely already done this work but, if you haven't, there's no time like the present.
A brand personality is what it sounds like, it is the intangible feeling, the emotion, the aura, of your brand. Think of Happy Days, remember the Fonz? He had the leather jacket, the hair, the "eeyyyy"... but he also had this indescribable thing too, this thing that made him the indelible Fonz that he was. You couldn't touch it, see it, or hear it, but it was there. He was the dependable rebel.
If the Fonz were a brand, he'd be Harley Davidson. And, more helpful here, if Harley Davidson were a person, it would be the Fonz. You might not agree with that, but I think you get the point either way :)
While your podcast has a lot of important and empirical attributes (microphones for example), in the next few sections we're going to talk about these intangibles... we're going to figure out what kind of man or woman your podcast would be if it were a human and not a podcast.