Water, despite the fact that it's incredibly common, is actually a pretty strange compound. Some of its stranger properties make it particularly useful for life, such as the way it switches from getting denser as it gets colder (normal) to getting less dense as it gets colder (not normal) below 4oC.
A recently discovered and even more recently characterized weirdness of water is that on the nano scale and on hydrophobic surfaces, water spontaneously flows in instead of being expelled the way one would expect based on the usual reaction of water to hydrophobic materials: (blue in the image below)
It turns out that way down on the nano scale, when you're dealing with just a few molecules at a time, just about everything gets weird. And this isn't even talking about quantum effects! That takes hold on even smaller scales, and is even weirder.
Carbon nanotubes have been a pretty sexy research topic in recent years, and graphene sheets seem to have recently caught up in news coverage. Both materials are made up of carbon arranged in a honeycomb pattern. In fact, carbon nanotubes are basically graphene sheets rolled into a tube.
In this case, when the tubes are about 1nm in diameter, water has to break many of the hydrogen bonds which keep it liquid at room temperature (and provide the reason for many of its weird properties - one of which is that it is liquid at room temperature) in order to fit into the tube. Breaking bonds takes energy, so one would expect that this would keep the water out of the nanotubes. Instead, the energy required to break the hydrogen bonds is more than made up for by the increase in entropy inside the nanotube.
One thing that immediately comes to mind when you have a material consisting of very small holes which water goes through easily is a filter. Current nanofiltration and reverse osmosis technology requires the dirty water to be pressurized in order to force it through the filter membrane. Since the water spontaneously enters these tubes, but the tubes are small enough to keep most things out (being about as big across as 3 water molecules), this should allow for much easier filtration.
Assuming, of course, that the water doesn't need to be forced out of the tubes on the other side of the filter.