An announcement is a message to your entire class.
To send an announcement, select the class you want to send to. You'll see a field for composing your message in the middle of your web account. When you click the blue "Send" button, everyone currently in this class will receive the announcement. Your participants will receive your announcement as a text, email or push notification depending on how they joined your class.
It's possible to send the same announcement to multiple classes at once, too. Just click "Add more classes" at the bottom of the screen once you have started typing the announcement.
A note about character limits:
Cell carriers limit text messages to 160 characters. 20 of these are used for your class name (announcement) or signature (conversation) to each message uses 20 of these, so that leaves 140 characters for your announcements.