The standard error of a proportion will be the largest it can be for a given $N$ when the proportion in question is $p=0.5$, and gets smaller the further the proportion is from $0.5$. I can see why this is so when I look at the equation for the standard error of a proportion, but I can't explain this any further. 

Is there an explanation beyond the mathematical properties of the formula? If so, why is there less uncertainty around estimated proportions (for a given $N$) as they get closer to $0$ or $1$?