Nihilism is the philosophical idea that all values are groundless and that nothing can be learned or communicated. To a true nihilist, existence (if there is such a thing) is meaningless. Therefore, moral choices, allegiances, aspirations, and all beliefs are also meaningless; neither life nor existence has any meaning.
Although few philosophers (and hopefully few people) would consider themselves completely nihilistic, the idea of nihilism is most closely associated with Friedrich Nietzsche, who saw it as a force leading humanity ultimately to moral, religious, and metaphysical catastrophe. You can discover more of Nietzsche's ideas about nihilism in Will to Power, a collection of his notes compiled by his sister after his death.
You can also find a more recent look at the conflict between Christianity and rampant nihilism in Eugene Rose's Nihilism: The Root of the Revolution of the Modern Age.