You must have a very small imagination then. Maybe you're talking about a very important Halloween decoration shaped like a spider. Maybe you're talking about an individual spider of an endangered species, and that spider is essential for the genetic viability of the species. Maybe you're talking about a whole species of spiders, and that species is necessary for the health of an ecosystem. Maybe you're in Hollywood talking about a whole group of spiders (say, tarantulas) and how they are necessary for a a movie you're shooting. Or... or... or...
Or perhaps we're talking about a certain spider that bit some guy named Peter Parker.
I trained my spider to defuse bombs. pretty useful if you travel to dangerous parts of the world.
Then it would not be indispensible considering the fact that you need the spider to treat its effects. Why not just erradicate the threat by making it dispensible. It's as though you are arguing the species benefits in solving its hazards. Just squash the damn bug already...lol
What if we were talking about how important the spider that bit Peter Parker was to the entire Spiderman franchise? Or the spider in Charlotte's Web? Or how happy a pet tarantula makes someone's son? Or a species of spider that keeps a human disease carrying pest down in a certain region? Or an MVP on the local sports team who are named the Spiders? Or as a French sentence that puts words together you should have already learned, in a syntax you should have already learned, as an exercise?
Maybe the spider is indispensable to control the other bugs that would overrun the place in the spider's absence.... That said, I personally can do without most spiders.
Can this refer to an entire species of spiders, like black widow or brown recluse?
Yes, I guess? In a situation like the following? « — Je n'aime pas les veuves noires, mais cette araignée est indispensable! » (note the change between plural and singular)
They offer grapnel as a choice as well as spider. But when I used it, grapnel was rejected. C'est fou.
1 Google result where this is used in a context other than language learning! https://www.google.fr/#q=%22Cette+araign%C3%A9e+est+indispensable.%22
Duolingo suggests grapnel as an alternate definition, which makes more sense, if you think about mountain climbers talking to each other, or an instructor talking to a mountain climbing student. Yet I was marked wrong for grapnel. A spider being indispensible? I had to google what a grapnel was, but when I saw it I was sure hat was the correct context.