You can! As you're in the Business Settings > Appointment Types page you can edit the confirmation message of each of your appointment types.
To do this, just click "Edit" to open the appointment type, then select “Show a message after scheduling…"
From there, a "Confirmation Message" box will pop up for you to edit. Here you can thank the client for booking with you, add information about the appointment scheduled, input your business contact info, whatever you'd like!
Links can also be added by clicking the icon, which is a great way to direct clients to a personal site after booking. Images can also be added using the icon.
Any information added to the confirmation message will display under the Cancel, Reschedule, and Edit Forms buttons on the appointment confirmation page. Kinda like this...
That information will also show within the event details if your client adds the appointment to an external calendar program like Google Calendar, iCal, or Outlook.
Here's a screenshot of what that looks like in Google Calendar: