So Just What is a Policy Anyway?

A policy is a compile-time mechanism for customising the behaviour of a special function, or a statistical distribution. With Policies you can control:

What action to take when an error occurs.
What happens when you call a function that is mathematically undefined (for example, if you ask for the mean of a Cauchy distribution).
What happens when you ask for a quantile of a discrete distribution.
Whether the library is allowed to internally promote float to double and double to long double in order to improve precision.
What precision to use when calculating the result.

Some of these policies could arguably be runtime variables, but then we couldn't use compile-time dispatch internally to select the best evaluation method for the given policies.

For this reason a Policy is a type: in fact it's an instance of the class template boost::math::policies::policy<>. This class is just a compile-time-container of user-selected policies (sometimes called a type-list):

using namespace boost::math::policies;
//
// Define a policy that sets ::errno on overflow, and does
// not promote double to long double internally:
//
typedef policy<domain_error<errno_on_error>, promote_double<false> > mypolicy;