The Participate button lets you sign up to take part in an event on the Calendar.

For signing up to events on the Calendar.

1- Go to the Calendar you are interested in. If it belongs to the portal, go to Tools in the menu on the left hand side of the portal's main page. If it belongs to a group, go to Groups > Group > Contents > Calendar.

2- Click on the Participate icon. You are automatically included in the list of participants for this event.
If you want to unsubscribe from an event you have signed up to, follow the same procedure, but this time a Don't participate button appears. Click on this to remove yourself from the list of participants.