Other forms: whirring; whirs
The softly vibrating sound of something moving fast is a whir. The whir of a hummingbird's wings up close sounds a lot like a buzzing insect.
Whir is one of those words like buzz, clink, and oink that sound exactly like what they mean; this effect is called onomatopoeia. You can use this one as a noun or a verb, so while your ceiling fan whirs overhead on a hot day, the whir of insects reminds you to close the window screen.