the number of conections can not obviously be more than even the number of atoms in the brain. but if each conection can have at least two posible states to be in, say on or off, then the number of different configurations, possible combinations of on's and off's is some hugh number like 100 trilion squared or factoral or something much bigger than my brain could ever understand.
if each possible conection patern is concidered a "brain State" then brain states is probably what the original speaker ment to say.