Traits are traits classes to determine the type of a derivative of another type.
For geometric objects the "geometric" derivative is chosen. For example the derivative of a Rotation matrix is NOT a 3x3 matrix containing the derivative of the elements of a rotation matrix. The derivative of the rotation matrix is a Vector corresponding the rotational velocity. Mostly used in template classes and routines to derive a correct type when needed.
You can see this as a compile-time lookuptable to find the type of the derivative.
Rotation R; Traits<Rotation> dR;