Bit of a big question there, and nihilism is a big concept—that often gets used quite loosely, to mean “relativistic” or “cynical”.
We are in a time in the West, of course, when a lot of longstanding moral absolutes have been increasingly questioned or scrutinised, and the outcome has been called nihilistic by both proponents and adversaries. (Adversaries more than proponents: the term is something of a cudgel.)
Nihilism has also been described as conspicuous in or constitutive of certain historical periods: for example, Jean Baudrillardand others have called postmodernity a nihilistic epoch; and some religious theologians and figures of religious authority have asserted that postmodernity and many aspects of modernity represent a rejection of theism, and that such rejection of theistic doctrine entails nihilism.
So one primary point of relevance is that it is a shorthand for the modern-day questioning of absolute values, which is prevalent, and which you need to be aware of to work out how the modern West ticks. Or fails to tick.
The second primary point of relevance is not as time-bound. Nihilism, like solipsism, is a useful intellectual exercise. It is a useful phase to go through, if you like. The teen or undergrad who stumbles across solipsism in their intellectual development is something of a cliche: “Woah, man, like what if I told you everything was, like, an illusion!”
But it is useful because, when you come out the other end, you acknowledge better the contingency and fragility of your construction of the world: you know to be on the lookout for misconstrual and bias better.
Same with nihilism. It’s good to have values. It’s better if you’ve scrutinised those values, and worked out why they are a good thing, rather than to just passively accept what you have been handed down. And a phase of questioning everything, of early nihilism, is useful to help you build them back up again—and convince yourself that there are things really worth holding on to, after all.