Typically falconers are training a bird to specific prey, sometimes one species, sometimes several. This ensures the bird, which is basically considered a type of hunting weapon in the eyes of the Wildlife Commission, only takes prey that it is currently legal to hunt. Of course, a hawk is not always 100% controllable and sometimes makes mistakes, but falconers are typically exempt from the occasional mishap of a bird taking illegal prey, provided the falconer reports the incident to the Commission.
This also enables falconers to train hawks to do specific jobs, such as abatement, where a falconer is hired by a landowner to hunt and remove pest species, like starlings for example.