Every single airplane toilet I've ever been to had the following (or similar) sign:
Why is drinking the tap water prohibited? And if drinking the water is prohibited, why is it acceptable to brush teeth using the very same tap?
tl;dr: The airplane "tap" water can be contaminated, to err on the safe side, don't drink it, don't use it to brush your teeth.
So apparently this article of the Wall Street Journal got it all started in 2002. An excerpt:
some little-noticed studies from Japan to the Netherlands have turned up some unfriendly bacteria in the tank water, including E. coli and the germ that causes Legionnaire's disease.
They also did some own testing with similarly distressing results:
contamination was the rule, not the exception: Almost all of the bacteria levels were tens, sometimes hundreds, of times above U.S. government limits.
According to the article it is also not uncommon that the water from the taps is served for people to drink when supplies of bottled water run out.
Apparently this prompted some action by the responsible U.S. government agency in 2004. However a quick google search turns out that test results aren't as nice even today as they should be: from 2009 to 2013/2014/2015 the theme seems to be recurring.
As a take-home message: to be safe, don't drink the tap water from the plane. Don't use it to brush your teeth. Bring a bottle of water on the plane or get bottled water from the flight attendants. If you want to play it really safe, use hand sanitizer after washing your hands in the loo.
You need to think of water tanks on the planes as being the same as those water coolers you see attached to the back of work trucks. They are constantly being refilled without being scrubbed out inside, overtime bacteria both noxious and harmless may build up inside.
The tanks on aircraft have an additional issue with being filled from multiple water sources, some of which may not be 100% perfect (especially those involved with international service to less developed areas).
Airlines contract to have potable water supplied to their aircraft, but as they know this is not 100% guaranteed safe, they preempt legal issues by labeling the water as such.
I have noticed less of these labels on newer or upgraded aircraft on recent fights. Perhaps they are adding a filtration system to the onboard water system.