Informal Description
The basic idea of bootstrapping is that the sample we have collected is often the best guess we have as to the shape of the population from which the sample was taken. For instance, a sample of observations with two peaks in its histogram would not be well approximated by a Gaussian or normal bell curve, which has only one peak. Therefore, instead of assuming a mathematical shape (like the normal curve or some other) for the population, we instead use the shape of the sample.
As an example, assume we are interested in the average (or mean) height of people worldwide. We cannot measure all the people in the global population, so instead we sample only a tiny part of it, and measure that. Assume the sample is of size N; that is, we measure the heights of N individuals. From that single sample, only one value of the mean can be obtained. In order to reason about the population, we need some sense of the variability of the mean that we have computed.
To use the simplest bootstrap technique, we take our original data set of N heights, and, using a computer, make a new sample (called a bootstrap sample) that is also of size N. This new sample is taken from the original using sampling with replacement so it is not identical with the original "real" sample. We repeat this a lot (maybe 1000 or 10,000 times), and for each of these bootstrap samples we compute its mean (each of these are called bootstrap estimates). We now have a histogram of bootstrap means. This provides an estimate of the shape of the distribution of the mean from which we can answer questions about how much the mean varies. (The method here, described for the mean, can be applied to almost any other statistic or estimator.)
The key principle of the bootstrap is to provide a way to simulate repeated observations from an unknown population using the obtained sample as a basis.
Read more about this topic: Bootstrapping (statistics)
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