What is Empirical distribution function, bootstrap?

The empirical distribution function of $X_1, \dots, X_n$ is $F_n(x) = \frac1n\#\{i: X_i \le x\}$, the law that puts mass $1/n$ on each observation. The bootstrap estimates the sampling law of a statistic $\hat\theta = T(X_1, \dots, X_n)$ by the law of $\hat\theta^* = T(X_1^*, \dots, X_n^*)$, where the $X_i^*$ are drawn independently from $F_n$, that is, with replacement from the data; in practice by computing $\hat\theta^*$ on $B$ resamples.