Going off of what Kim said, you can work directly at an events company to help do events for other companies, or go internal and work events for a specific company. I'm an office coordinator and do some light event planning for our company, in addition to other responsibilities like employee wellness, employee recognition, facilities, and other administrative work.
Event planning can take you in many different directions. One area would be things like weddings, debuts, etc. Another might be company Christmas parties, annual award banquets, etc. Living in a tourist city, we have lots of conventions. The hotel staff has people that make sure it all goes smoothly, booking the rooms, and handling all the arrangements. And the city has positions at the Convention and Tourism department that also help plan events - including when a movie crew wants to come in and shoot scenes - requiring closing streets, etc. Some of this might fall under the broad heading of "hospitality industry" rather than specifically under "event planning." But these are some things that I can think of. Hope it has helped.