The class Kernel_traits<T> provides access to the kernel model to which the argument type T belongs. (Provided T belongs to some kernel model.) The default implementation assumes there is a local type T::Kernel referring to the kernel model of T. If this type does not exist, a specialization of Kernel_traits<T> can be used to provide the desired information.
This class is, for example, useful in the following context. Assume you want to write a generic function that accepts two points $$p and $$q as argument and constructs the line segment between $$p and $$q. In order to specify the return type of this function, you need to know what is the segment type corresponding to the Point type representing $$p and $$q. Using Kernel_traits<T>, this can be done as follows.
template < class Point > typename Kernel_traits<Point>::Kernel::Segment construct_segment(Point p, Point q) { ... }

 If T is a type K::Point_2 of some kernel model K, then Kernel is equal to K. 