VERY new. As Sattik says, fresh from the factory or shop.
He's bought a brand new car! He must be rich! (We could simply say, "He's bought a new car!" But the BRAND NEW gives emphasis to the newness)
I've a pair of brand new trainers for running.
Oh that's a nice sofa! It looks brand new. (It might not actually be new, but it LOOKS that way)
I'm tired of my old clothes. I want some brand new ones!
We don't usually use the word brand when talking about people, animals, or food. You wouldn't say, "I've got a brand new pizza," or "I've got a brand new dog."
But we do say things like, "She's got a brand new hairstyle." Perhaps to emphasize it's not just a little different but very different.