The way it works in the entertainment industry is:
Agents get what is called a breakdown. This is a listing of the various projects being cast, what they are looking for, and who is casting them.
An agent will submit an actors headshot and resume to the casting director for any talent they have that matches the description.
The casting director will review these headshots and resumes and call in talent they wish to see. The casting director will reach out to the agent to set up an audition.
The agent will reach out to the actor with the audition information and confirm the interest and availability with the actor and inform casting. The audition information will include when, where, character description, sides to prepare and any other additional information from casting. If it is not an in room audition the information will include self tape instructions and deadlines for the self tape.
For in room theatrical auditions the talent is expected to come in with an 8x10 printed headshot with a resume attached to the back (facing outward so the casting director sees it at a glance). Always bring a headshot unless otherwise stated on the email you receive from the agent.
For commercial auditions headshots are not usually requested as most use digital avenues for headshots. But an actor should have headshots with them even if they are in the car. No actor should walk into a meeting or audition without headshots near by.
The basic purpose of that headshot is to get you in the door for the auditions. Above is the basic work flow of the headshot. But Headshots are used in other ways too. For example, any production office will have a board that has the headshot of the actor and the role that they are playing hanging in a public space. The wardrobe department and the hair and makeup departments will also often hang headshots in their spaces for their work flows. Headshots are used for announcements in trade magazines such as Deadline, Variety, Hollywood Reporter and so forth. They are used on marquee boards for comedy clubs and theaters. Headshots are the images that are used to promote actors not only to agents and casting directors but in random other ways throughout the industry.