Please explain an "unwritten constitution" to this American

OK, so it has a LOT of problems and is clearly under threat at the moment, but we do have a Constitution of the United States. It is written down and widely published, and it is supposed to be the "supreme law of the land", overruling all other laws in the case of conflict. Our Supreme Court exists to decide whether all other laws are Constitutional, when a conflict is claimed.

I always hear that the UK has an "unwritten constitution," but I've never really grasped how this is supposed to work. We have enough trouble agreeing on interpretation/application of our written Constitution; how on earth do you do it with an unwritten one? Don't most countries these days have a written constitution?