Cove needs to pair with the Cove app periodically. If it's time to pair Cove, an orange LED will appear when you try to start a session, even if Cove is fully charged. Until you pair Cove, you will not be able to start a session offline.
Just pair Cove with the Cove app, and start a session by pressing the Cove button on the Home tab.
Pairing Cove is important to:
Keep your session history up to date
Check for updates to Cove's firmware
Make sure that Cove is running its best