In dynamical systems, there are two major entropies used, topological and metric. They each quantify, in technically different ways, how complexity of orbits grows as their length is allowed to grow into infinity. To make things slightly more precise, topological entropy measures the number of orbits that can be distinguished if we measured the position of points up to a fixed resolutions, and then let the resolution get finer and finer, and orbit length get longer and longer. A fairly good, not-so-technical introduction to both topological and metric entropies was given by Lai Sang-Young in Entropy in dynamical systems, available here: http://cims.nyu.edu/~lsy/papers/entropy.pdf