When people invite you to events using Google Calendar, these events will automatically appear on your calendar with a respond arrow next to the event name. To RSVP directly on your calendar, follow these steps:
If you'd like to change your attendance status, revisit the event's page and click on Change your response.
You'll also get an email with the text of the invitation. If you're a Gmail user, you can RSVP to the event directly through the email invitation.