This probably seems like a dumb question but how does a hardwood floor expand if it is nailed down?

We are going to be installing brazilian walnut floors and everything I have read says that we need 3/4" gap around all walls, is this correct?

I'm sure I will have a lot more questions to follow as I search for answers here but am not sucessful in finding exact answers.

Thank you in advance.

Very rarely will a perimeter expansion be taken up, when a floor swells. The boards cup from compression, and then heave out in the middle of the installation somewhere.

The ¾ is for a massive flood and the wood swelling and pushing your walls off the foundation.

A 3% gain in moisture content can equal to 2" of dimensional gain, over just 10 feet of Red Oak flooring.

Thank you for explaining that. I have read on some sites too that 1/2" gap is recommended, but what would be best for brazilian walnut, 3/4" or 1/2"?

You can leave any gap you like. The key is keeping a consistent humidity level inside your home, for acclimation, installation and the life of that floor.