What is the expectation maximization algorithm?

@article{Do2008WhatIT,
  title={What is the expectation maximization algorithm?},
  author={Chuong B. Do and Serafim Batzoglou},
  journal={Nature Biotechnology},
  year={2008},
  volume={26},
  pages={897-899}
}
The expectation maximization algorithm arises in many computational biology applications that involve probabilistic models. What is it good for, and how does it work? 
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