No one's ever been able to explain story points to me without saying something like "Story points are kind of like how long it will take to implement, except it's not that".

So what is it then? All the explanations and examples are in units of time, but with a disclaimer saying that the true nature of story points is not time-based, except for the fact that they can only be explained in terms of time.

I've always asked for it when joining a team to calibrate my story point estimates. At some teams 1 point is about a half hour task and at other teams it's a full day.