What it means
Zoom means to move crazy fast or do something in a rush, with that whooshy, blink-and-it's-gone feel. You can zoom off in a car, zoom home on your bike, or zoom through a bit of work when you're trying to get it done sharpish. It's a much older everyday word than the video app, so the meaning usually comes from the situation.
Usage examples
"She zoomed through that exam, slapped it on the desk, then nipped to Greggs. Invigilator looked rattled, like she’d either revised or guessed the lot."
"I'll zoom to the shop before it shuts, back in five with the milk."
"She zoomed off on her bike the second the bell rang, no goodbye or anything."
"We were already late, so he just zoomed out the house with one trainer half on and toast in his hand."
"I need to zoom through these emails before lunch or they'll start breeding in my inbox."
Where it comes from
Zoom showed up in English in the late 1800s as an imitative word for a deep humming or rushing sound, the sort of noise you hear from fast movement. That soundy little word then stretched naturally into the verb sense of moving very quickly, and later into blasting through tasks at speed too.