Clicking the "Add to Calendar" button downloads an ICS file which allows you to add the corresponding event to your personal smartphone calendar, Google Calendar, or applications such as Microsoft Outlook. However, not all applications are compatible with ICS files.
A file with the ICS file extension is an iCalendar file. These are plain text files that include calendar event details like a description, beginning and ending times, location, etc.
For most user's, simply opening the ICS file will launch a corresponding calendar application allowing you to save the event.
For more information on working with ICS files, check out https://www.lifewire.com/ics-file-2622749.