Hey Tess,
Thanks for reaching out – your language indeed makes sense 🙂 and yes, in general events made The Events Calendar will be “shareable” to apps on your phone.
Now, I say “in general” because there are really only two export buttons provided: Google Calendar, and the iCal export. Here’s a screenshot of these two buttons, for an idea of what they look like: https://cloudup.com/cPJGtuXqVbJ.
So, every calendar app under the sun might not be supported, but these two calendar services are. This is because they’re the main ones these days (Outlook is huge, too, but not specifically supported by The Events Calendar at this time), and because Outlook and other apps are harder to send event data too.
For a direct example, I strongly encourage you to check out our demo site http://wpshindig.com on your smart phone. Check out this event, for example, and try using the Google Calendar and/or iCal links just for testing purposes → http://wpshindig.com/event/wordpress-topanga-meetup/2015-07-16/
I hope this all helps – let us know if it does, or if you have any other questions!
– George