The focal point of a spherical mirror is defined as the point where reflected rays converge when they are incident parallel to the principal axis. If the incident rays are parallel to each other but not parallel to the principal axis, then they will converge to a point in the focal plane. When light is reflected from a spherical mirror it obeys the same laws of reflections as when reflected from a plane mirror. In general, to construct a ray diagram, we would need to measure angles before drawing the rays. This could be a tedious process.
Principle rays result from optical properties of the mirror.
For example, we know that any ray incident parallel to the principal axis will be reflected through the focal point. Such rays form a set of principle rays and can be drawn without to measuring angles. Likewise, because of the principle of reversibility, any ray incident through the focal point will be reflected along a line parallel to the principal axis. Again, rays incident through the focal point form another set of principle rays. Also, we know that all radial lines are normal to the mirrors surface, therefore, any ray incident through the center of curvature will be traveling along a radial line and will be reflected back onto itself.