<p>Other answers being good, i will try to provide another perspective and tackle the intuitive part of the question.</p>

<p><a href="http://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm" rel="nofollow">EM (Expectation-Maximization) algorithm</a> is a variant of a class of iterative algorithms using <a href="http://en.wikipedia.org/wiki/Duality_%28mathematics%29" rel="nofollow">duality</a></p>

<p>Excerpt (emphasis mine):</p>

<blockquote>
  <p>In mathematics, a duality, generally speaking, translates concepts,
  theorems or mathematical structures into other concepts, theorems or
  structures, in a one-to-one fashion, often (but not always) by means
  of an involution operation: if the dual of A is B, then the dual of B
  is A. Such involutions <strong>sometimes have fixed points</strong>, so that the dual
  of A is A itself</p>
</blockquote>

<p>Usually a <em>dual</em> B of an <em>object</em> A is related to A in some way that preserves some <em>symmetry or compatibility</em>. For example AB = <strong>const</strong></p>

<p>Examples of iterative algorithms, employing duality (in the previous sense) are:</p>

<ol>
<li><a href="http://en.wikipedia.org/wiki/Euclidean_algorithm" rel="nofollow">Euclidean algorithm for Greatest Common Divisor, and its variants</a></li>
<li><a href="http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process" rel="nofollow">Gram–Schmidt Vector Basis algorithm and variants</a></li>
<li><a href="http://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean" rel="nofollow">Arithmetic Mean - Geometric Mean Inequality, and its variants</a></li>
<li><a href="http://arxiv.org/pdf/1105.1476.pdf" rel="nofollow">Expectation-Maximization algorithm and its variants</a> (see also <a href="http://www.researchgate.net/profile/Shun_Ichi_Amari/publication/222444851_Information_geometry_of_the_EM_and_em_algorithms_for_neural_networks/links/0f3175385938a75a6c000000.pdf" rel="nofollow">here for an information-geometric view</a>)</li>
<li>(.. other similar algorithms..)</li>
</ol>

<p>In a similar fashion, <a href="http://www.cs.toronto.edu/~fritz/absps/emk.pdf" rel="nofollow">the EM algorithm can also be seen as two dual maximization steps</a>:</p>

<blockquote>
  <p>..[EM] is seen as maximizing a joint function of the parameters and of
  the distribution over the unobserved variables.. The E-step maximizes
  this function with respect to the distribution over the unobserved
  variables; the M-step with respect to the parameters..</p>
</blockquote>

<p>In an iterative algorithm using duality there is the explicit (or implicit) assumption of an equilibrium (or fixed) point of convergence (for EM this is proved using Jensen's inequality)</p>

<p>So the outline of such algorithms is:</p>

<ol>
<li><strong>E-like step:</strong> Find best solution <strong>x</strong> with respect to given <strong>y</strong> being held constant.</li>
<li><strong>M-like step (dual):</strong> Find best solution <strong>y</strong> with respect to <strong>x</strong> (as computed in previous step) being held constant.</li>
<li><strong>Criterion of Termination/Convergence step:</strong> Repeat steps 1, 2 with the updated values of <strong>x</strong>,<strong>y</strong> until convergence (or specified number of iterations is reached)</li>
</ol>

<p><strong>Note</strong> that when such an algorithm converges to a (global) optimum, it has found a configuration which is <strong>best in both senses</strong> (i.e in both the <strong>x</strong> domain/parameters and the <strong>y</strong> domain/parameters). However the algorithm can just find a <em>local</em> optimum and not the <em>global</em> optimum.</p>

<p>i would say this is the intuitive description of the outline of the algorithm</p>

<p>For the statistical arguments and applications, other answers have given good explanations (check also references in this answer)</p>
What is an intuitive explanation of the Expectation Maximization technique?
<p>Expectation Maximization (EM) is a kind of probabilistic method to classify data. Please correct me if I am wrong if it is not a classifier. </p>

<p>What is an intuitive explanation of this EM technique? What is <code>expectation</code> here and what is being <code>maximized</code>?</p>