Bootstrap resampling is a computational technique for measuring how reliable a statistic is, introduced by Bradley Efron in his 1979 paper Bootstrap Methods: Another Look at the Jackknife. The problem it solves is universal: you compute some number from your data, such as an average, a median, or a model coefficient, and you want to know how much that number would change if you had collected a different sample. Classical statistics answered this with formulas that exist only for simple cases.
The bootstrap replaces those formulas with brute-force resampling. It treats your single observed sample as a miniature stand-in for the whole population, then repeatedly draws new datasets of the same size by sampling from it with replacement, so some original points appear several times and others not at all. The statistic of interest is recomputed on each resampled dataset, and the variation across all these recomputations estimates its true uncertainty.
The procedure works for essentially any statistic, however complicated, because it never needs to know the analytic form of the statistic’s sampling distribution. Efron also showed the older jackknife method is a linear approximation to it.
Bootstrap resampling matters because it made honest uncertainty estimates cheap and universal. It is widely used to put confidence intervals around predictions, and the same resampling idea drives ensemble methods like bagging and random forests, where many models trained on bootstrap samples are combined for more stable performance.