Make sure you're using the Garmin Connect app to pair and not the Bluetooth settings on the iPhone. If you've already paired with the iPhone, I suggest starting over and following this process.
From the main menu on your iPhone
Open Settings >> Bluetooth
Under "MY DEVICES" tap the "i" icon to the right of your Garmin device
Tap "Forget This Device"
Restart your iPhone
Open the Garmin Connect Mobile app
Tap the "+" icon in the upper right
Select your device from the list of Garmin devices
Put your Garmin device in Bluetooth pairing mode (This varies based on device. For the Explore 820 Settings > Bluetooth > Enable > Pair Smartphone)
Tap Start on the app and the iPhone
When prompted with "Bluetooth Pairing Request" enter the PIN (passkey) displayed on your Garmin device
When iPhone displays "Pairing Complete!" tap "Done"
