It's about perspective. It's about how the world looks to your characters. If you're writing about nonhuman beings, or even humans from a vastly different culture, you might need new words for the concepts that affect their lives.
I mean, say that your characters are prey animals of some sort. That doesn't just mean that they'll think about predators a lot. It means that their entire concept of predators is a little bit different from ours. There's no sense that a hawk or a cat is a beautiful thing. There's no acknowledgment that foxes are vital to the ecosystem. Predators are enemies. So, as an author, you might decide to make up a new word that means "member of an enemy species."
Or say your characters have an emotion that humans don't often experience. Like, say, a weird mixture of terror and apathy, a sort of waking coma that comes from being spooked again and again until you're completely exhausted. If it happens often—with prey animals, it might—there should be a short and simple word for it.
To people who've read it, it's probably fairly obvious that I'm talking about Watership Down. In my opinion, this book is a pretty good example of how invented language should be used. It doesn't take over the story and it doesn't really require a glossary (although the editions I've owned have had one). It arises naturally from the way the characters think. It helps the reader enter into their viewpoint. And, as a bonus, when one of the characters cusses out the villain—entirely in the invented language—the reader has been drawn into the setting far enough to make it feel like real, human swearing. This despite the fact that one of the obscenities just means, "smells like a fox."
(As if it isn't obvious, I'm a huge fan.)
Izunya