For me, an independent brand is a brand that is in it for the sake of progressing the art of horology rather than a company whose motive is pure profit. Granted, you must make money, but independent brands seem to care more for their art than the money the receive.
I also feel that I ndependent brands tend to be more passionate with regard to all aspects of horology.
They are more one-on-one with their patrons. The individual buying the piece doesn’t just contact a representative of the brand, but they have the ability, in most cases, to speak directly to the watchmaker. I feel that you end up with a watch that you have a deeper connection to. One that goes beyond a brand.
Is there a single definition? IMO, no.
I do feel however, that they seem to fit a mold of accessibility and they have an incredible passion for the art and history of watchmaking. They also tend to push boundaries and further the science when compared to “big” brands.
*thoughts by me, spelling by Siri.