...it acts exactly like regular matter in that it has gravity. So the amount of dark matter in a galaxy is measured as a mass, that is, it is measured by the amount of gravitational attraction it generates (which can be observed by its effects on normal matter).

So for example, the rotation of a galaxy is determined by the total amount of matter it contains, although we can only see the luminous part of that matter in order to determine the rotation. Also, clusters of galaxies should fly apart, unless they contain much more matter than can actually be seen. That's how dark matter was discovered in the first place, it was noticed that their gravitational interaction was NOT determined by Kepler's and Newton's laws. They seemed to have much more matter than was actually there.

Now, it isn't absolutely certain there is such a thing as "dark matter". Perhaps this gravitational discrepancy we see is caused by something else; perhaps the law of gravity operates differently over large distances, or maybe there is something else entirely going on we haven't thought of yet. But it appears that today, the explanation that best fits the facts is that most of the matter in the universe is invisible, and it can only be detected by its gravitational effect on the visible matter (stars, gas, dust, etc).

If dark matter is indeed invisible matter, we still have no clear idea what it might be. Perhaps it is composed of Weakly Interactive Massive Particles (WIMPS) like neutrinos. Another suggestion is that it may be the gravitational effects of large amounts of ordinary matter lumps of a size that cannot be observed (too cold to give off any radiation) but too small to cast shadows, concentrated in the outer regions of galaxies, MACHOS (MAssive Compact Halo Objects). But nobody really knows, and both of those hypotheses fail to explain all the observations satisfactorily. All we know for sure is that the universe seems to contain a lot more matter than we can see, and as your article indicates, that matter interacts with visible matter gravitationally, in a predictable way.

Oh, and another thing. Dark Matter doesn't seem to be connected in any way to Dark Energy. But that's something else altogether.