Sometimes discrete models are easier to work with, and it is important to have well-thought out discrete maps that are expected to exhibit *generic phenomena* that any dynamical system -- or at least a particular class -- of discrete or continuous dynamical systems have.

One example that comes to mind is the Standard Map (http://en.wikipedia.org/wiki/Standard_map):  It is much easier to do numerical simulations for this map than solving a 2nd order time-periodic PDE, yet the dynamical phenomena observed in this map is very universal.  For example, the same behavior exists in the periodically forced pendulum.  It is also used in plasma physics, statistical mechanics, etc. as a toy model to work with.

Aslo, whenever one simulates an ODE or PDE, one is essentially applying a discrete map.  To elaborate, consider the ODE

$\dot{x} = v(x, t)$

Many numerical schemes to solve the ODE is of the form

 $ x_{n + 1} = x_n + f(x_n, h)$

Where $f$ is a map that takes one from the current time step at position $x_n$ to $x_{n + 1}$ and $h$ is a time-step.  Thus, $f$ is really a discrete map.  The same goes when discretizing a PDE in space and/or time.  When analyzing a numerical scheme it is important to make sure the dynamics of the numerical scheme match the dynamics of the system.