Invitations
Inviting contacts to events
When creating an event, tap Show Details to see the invitees field. You can add an email address or search for any contacts you have in the Contacts app and invite them to your event. Tap Check Availability in the upper-right to see your invitee(s) schedules, and use the "Next Available Time" button to automatically create your invite for the next free slot that coincides with you and your invitee(s) schedules.
Sharing events
If you want to share an event with someone without inviting them to it directly, you can hold your finger on the event and tap ‘Share’ to email the event to another person.