What it means
A tiff is a small argument, the sort where people get a bit snippy, go quiet, throw a couple of icy looks, then usually get over it once the mood unclenches. It's for petty fallout between partners, mates, or family, not some full-scale screaming breakup situation.
Usage examples
"Me and my sister had a tiff over the last biscuit, then Dad stuck the kettle on and we were laughing again in five."
"My parents had a tiff over the shopping list at the supermarket and didn't speak the whole drive home."
"It was just a tiff about the colour of the bridesmaids' dresses, the bride had already let it go by the next morning."
"We had a proper little tiff over who left the kitchen in a state, then acted normal again ten minutes later."
"Don't worry, they're not breaking up, it's just a tiff about where to go for Christmas."
Where it comes from
Recorded in English since the early 1700s, tiff first meant a little fit of temper or a slight offence taken. It later settled into the sense it still has now, a minor quarrel or brief falling-out that flares up, sulks for a minute, then usually blows over.