What does it mean when they say the neck has a 12" radius? I have also seen 9" on some ads.

Basically a 12" radius is the contour of the freatboard. If you take that contour and extended it, it would make a 12" circle so what you have on your fretboard is a small section of that imaginary circle. So a 17" freatbord would be flatter as the circle is bigger and a 9" would have more curve as the circle is smaller given you have the same freatbord with. If you want more details look here.

http://www.musicplayer.com/article/fretboard-radius/Sep-06/23104

Also you would get a faster response if you placed this question on the right forum (Basses). Hope this helps.