Why Bootstrapping Works

The gray histogram below depicts a random sample from of 1000 observations from a standard normal distribution (red curve).

We’d like to resample from the population (the red curve), but we can’t, because all we have is the sample (the gray histogram). But look how closely the distribtion of the sample resembles the distribution of the population. It would seem that resampling from this empirical distribution is almost as good as resampling from the original population. No?