In classical statistics, confidence intervals and hypothesis tests rely on making distributional assumptions about the data generating process. Often, these assumptions are incorrect. The bootstrap and related techniques rely on resampling from the data to construct the required distributions, and thus they are guaranteed to be correct given sufficient data. These techniques don't work very well with a small number of data points, but they are extremely effective in the era of big data.
Recommended Books

An Introduction to the Bootstrap
Bradley Efron and Robert J. Tibshirani
Key Features
 Intext exercises
Key Topics
 Adaptive Estimation
 Approximate Likelihoods
 Bootstrap Confidence Intervals
 Bootstrap Estimate of Bias
 Bootstrap Estimate of Standard Error
 Bootstrap Hypothesis Testing
 Bootstrap for Regression Models
 Connections Between the Bootstrap and Classical Inference
 Cross Validation
 Efficient Bootstrap Computation
 Error in Bootstrap Estimates
 Geometry of the Bootstrap
 Parametric Bootstrap
 Permutation Tests
 PlugIn Principle
 Practical Considerations When Using the Bootstrap
 The Jackknife
Description
This is a great introduction to the bootstrap from its creator. It's quite gentle as statistical books go; the more challenging mathematics are relegated to the end of the book. Bootstrap hypothesis testing and confidence intervals receive excellent coverage, along with permutation testing, the jackknife, and other bootstraprelated topics. There is code that is written in the now largely defunct S language (the progenitor of R). It translates easily to R.