For example, you have a plant you can't identify. Hard to Google search with words. "Plant with small red berries and...". You could reverse image search your photo of it, probably won't help either. Show an LLM the photo (some accept images now). LLM tells you what it thinks. Now you Google search "Ribes rubrum" to verify it. Much easier.
You've got a complicated medical problem that's been going on for months. A google search of all the factors involved would be excessively long and throw up all sorts of random stuff. You describe the whole scenario to an LLM and it gives you four ideas. You can now search those specific conditions and see how well they actually match.
I've found there are actually a lot of questions that fit in that sort of NP complexity category.