I'm not going to pretend to be the authority on dark matter here, but neither should most of the people posting in this thread who are clearly assuming quite a bit.
It sounds like he was partially right. Most people know that the majority of an atom is empty space; however, that doesn't mean that empty space doesn't weigh anything. This is where dark matter and dark energy come into play, because all of weight of atoms in a human body that can be measured don't account for a large majority of our mass. Recently, scientists have started to change the way they think about empty space...perhaps it's not really empty after all; rather, it's a frothing, highly excited field of dark energy that is waiting to pop into existence.
Well dorkydood, you are mostly wrong :-).
"because all of weight of atoms in a human body that can be measured don't account for a large majority of our mass."
Like i (and other) have allready written, relativistic/QFT corrections to the *rest mass* of quarks in the elementary particles account for the great majority of their mass. but this has nothing to do with space inside an atom, it has to do with the energy in gluon fields which are there because, well, there are quarks. I will give you that the weight of the atoms in your body do not add up to your mass, but if you divide by the gravitational acceleration they do ;-).
on the large scale there is dark energy which can be observed (indirectly) on the cosmic scale, but that is something else entirely.
Perhaps to illustrate why the statement by the speaker must be wrong: Suppose that "empty space" really did account for 90% of the mass of an atom. This mean ALL empty space roughly have the same density of an atom, in other words, the universe would collapse to a black hole in no time (or rather, it would allready be a giant black hole). Since we are not all dead, that is not the case.
James_Woods: The emperical status of dark matter is not as bleak as it is often laid out in popular science, see for instance: http://en.wikipedia.org/wiki/Dark_matter#Observational_evidence. True none of these are /direct/ measurements (but neither did we have direct measurements of the neutrino for quite some time), and some can be explained alternatively, but together they paint a pretty suggestive picture and i think it is fair to say that at this time the simplest explanation is dark matter.