What it means
If two people, ideas, or situations are poles apart, they're at total opposite ends and there's basically no overlap. It's what you say when the gap isn't tiny or fixable, it's massive, proper north-versus-south energy.
Usage examples
"On politics they are poles apart, yet somehow they have stayed best friends for thirty years."
"My two brothers are poles apart on every subject from football to flat-pack furniture, the older one supports Manchester United, the younger Manchester City, and the Sunday lunch table at our mother’s house is a small geopolitical event every weekend in November."
"The Brexit conversation around the office kitchen at break time leaves the team poles apart still, six years after the referendum, and the manager has put up a tactful notice asking colleagues to stick to the cricket and the weather over the kettle and the biscuit tin."
"Me and my flatmate are poles apart on holidays. I want a quiet cottage and a book, he wants three airports, no sleep, and a tattoo by Tuesday."
"They looked cute for about ten minutes, then you heard them talk about money and realised they were poles apart from the jump."
Where it comes from
It comes from the literal North and South Poles, the two opposite ends of the Earth. English has used poles apart figuratively since at least the 18th century to talk about people, opinions, or things that sit at completely opposite extremes. Nice clean image, no mystery sauce needed.
