First, you need to create a category. You do that by going to your organization and clicking "settings" -> "categories" -> "add category". Name the category and finish by clicking "save".
When you've created the category, you click "pages" -> the name of the category (house icon). Click the block named "organization-events". Under ”only show events from these categories” you select the new category you've created.
Now you're able to categorize your events.
When you create an event you're now able to, under "settings" -> "setup" choose for the event to belong to the category you've created. It will then appear on the display site.
The events can have different "viewer access" even though they're shown on the display site. This is also adjusted under "settings" -> ”setup”. It can be "everyone", "invitation only" or "password".