External means outside our heads. Its there even if we aren't. Independent means our culture or color shouldn't matter. The EIOR is the same for everyone even extra terrestrials. Objective means there is a way of asking questions about it that provides universally true answers.
Reality means what exists, what truely is.
It is what many of scientists think we are reaching and can, in fact, get hold of. Science claims to be able to find truths about physical reality that are universal and objective meaning they do not change with time. It is difficult to say if an EIOR really exists. Also how can one doubt that science isn't reaching some kind of truth given the technology it has created. On the other hand when one deals with something as complicated as the Big Bang Theory or sub-atomic particles is it possible that our theories are ornate enough to be standing in the way of a view of what is real.