Many anarchists, particularly within the Individualist, illegalist, egoist, insurrectionist etc tendencies tend to have a nihilist bent. We are not fooled by delusions of an anarchist revolution, and if one were to even happen we have no faith that it would be a revolution in which we all got along afterwards. However, unlike many revolutionary anarchists, we don't see this as a reason to stop fighting for our desires. Somebody could prove to us today that there would never be a revolution, and we would still do what we do. Many of us don't even desire a revolution, for reasons which are too dynamic to get into right before I go to sleep.*
Aside from the (non) revolutionary aspect, we are also moral nihilists and don't fall prey to the moral and dogmatic crusades of the left (and left anarchists).
Basically, anarcho-nihilism is the tendency to inject a healthy dose of nihilism (positive nihilism, generally) into different aspects your anarchism. And in my opinion you can't actually have productive or effective anarchism without this.
People don't generally identify as "nihilists" the way one would identify as a vegetarian, atheist etc. it's more of a tendency.
Renzo Novatore was an anarchist who talked a lot about his nihilism. Nihilist aspects can also be found in Stirner's writings. There is of course Nietzsche, who was not an anarchist but whom many anarchists find inspiration in.
Little Black Cart publish a handful of books dealing with nihilism from an anarchist perspective. Check out Boom!, Attentat, and blessed is the flame, which is a particularly fascinating book which looks at concentration camp rebellion through an anarcho-nihilist lens. Also check out the recent writings of the CCF.
This wasn't the most thorough response I could give, but it's bedtime. I'm sure somebody else will come along with a more intelligent way to frame all of this. I'll just leave you with this quote from Novatore's I Am Also A Nihilist:
I am an individualist because I am an anarchist; and I am an anarchist because I am a nihilist. But I also understand nihilism in my own way...
I don’t care whether it is Nordic or Oriental, nor whether or not is has a historical, political, practical tradition, or a theoretical, philosophical, spiritual, intellectual one. I call myself a nihilist because I know that nihilism means negation.
Negation of every society, of every cult, of every rule and of every religion. But I don’t yearn for Nirvana, any more than I long for Schopenhauer’s desperate and powerless pessimism, which is a worse thing than the violent renunciation of life itself. Mine is an enthusiastic and dionysian pessimism, like a flame that sets my vital exuberance ablaze, that mocks at any theoretical, scientific or moral prison.
And if I call myself an individualist anarchist, an iconoclast and a nihilist, it is precisely because I believe that in these adjectives there is the highest and most complete expression of my willful and reckless individuality that, like an overflowing river, wants to expand, impetuously sweeping away dikes and hedges, until it crashes into a granite boulder, shattering and breaking up in its turn. I do not renounce life. I exalt and sing it.
*I should note that I can't speak for everybody as far as the revolutionary stuff goes, but it is the general opinion of most anarchists I have spoken to who tend towards nihilism.