There are 3 ways to complete an event.
You can edit an event status by clicking on the event from the calendar:
You will be shown a dialogue to edit:
You can edit multiple events at once by clicking on the grid view button. From here you can quick change the category, status and assignment of multiple events.
You can complete an event that is associated to a site when submitting an inspection such as a site service. If there are events scheduled for the site you will be shown a dialogue at the end of the inspection report which will allow you to check-off the events to complete:
By checking off the event as complete, it will be marked as complete on your calendar: