Think of a non-emergency as the annoying sibling of a real emergency. It’s a problem that needs police attention, but nobody is bleeding, there’s no fire, and the suspect isn’t currently doing a dramatic car chase through your backyard. Examples include: your car got broken into last night (but the thief left you a weird note), someone stole your garden gnome collection, or you heard loud music at 2 AM from a party that’s technically legal but also very rude.
Also, reporting lost property—like that one sock you swear had sentimental value—is a non-emergency. And please, for the love of all that is peaceful, do not call 911 to ask if the power is out. The dispatcher cannot see your fuse box from their desk.