What it means
Zany is for someone or something wildly silly, hyper, and entertaining in a harmless way. Not sinister, not properly unhinged, just running on cartoon-goblin energy and loving every second of it. You hear it for chaotic comedy, daft behaviour, or anything so goofy it feels one step away from a pratfall.
Usage examples
"He joined the video call in a wizard hat, shouting made-up spells at the printer. Everyone cracked up, it was pure zany energy."
"My cousin runs a zany cocktail bar in Bristol, the menu is written in haiku, the bartender wears different sunglasses every day, and the drinks come with miniature umbrellas that match the wallpaper of the bathroom in some cosmic way."
"The school nativity took a zany turn when the lamb costumes arrived two sizes too big, the five-year-old shepherd lost a slipper halfway up the aisle, and the angel decided to introduce her solo with a magic trick involving a rabbit."
"That party went fully zany once Dan turned up with a karaoke machine and a traffic cone on his head."
"The film's a bit messy, but the zany bits are exactly what make it fun to watch with your mates."
Where it comes from
It comes from Italian zanni, the stock comic servant from commedia dell’arte. English picked it up in the 1500s through theatre talk, where a zany was the clownish sidekick doing exaggerated nonsense. Later it stretched into the everyday adjective for playful, madcap, high-energy silliness.