What is the Asymptotic Equipartition Property (AEP)?
When you are sampling a stochastic process $n$ times, the larger you make $n$, the higher the probability that the series of samples is contained in the so called strongly typical set of outcomes of length $n$, where all members have roughly the same probability to be realized. If you let $n\rightarrow \infty$ it holds that
$$-\frac{1}{n}\log p(X_1,X_2,...,X_n)\rightarrow H(X)$$
with $H(X)$ being the entropy rate of the process. 

This should be intuitively clear: the longer the sequence, the more possible outcomes, each with possiblity near zero but positive. The number of typical outcomes with $p\approx\epsilon$ is growing faster than the number of non typical outcomes as $n$ is growing. As $n\rightarrow \infty$, the "leftover probability" for non typical outcomes gets smaller and smaller, thus making the above equation valid.