I think it means "for any given point in the specified area, and for any given point in time, p(rain)=50% So it of course won't rain for exactly 50% of the tim

I think it means "for any given point in the specified area, and for any given point in time, p(rain)=50% So it of course won't rain for exactly 50% of the time on a given day, but over the long run, it will.