The blue light on my Apple TV flashes very fast and the screen displays a cord needs to be inserted beneath the hdmi slot and connect to the iTunes icon. What do I need to do?

Welcome to the Apple Community.

If your problem persists get yourself a micro USB cable (sold separately), you can restore your Apple TV from iTunes:

1. Remove ALL cables from Apple TV. (if you don't you will not see Apple TV in the iTunes Source list)
2. Connect the micro USB cable to the Apple TV and to your computer.
3. Reconnect the power cable (only for Apple TV 3)
4. Open iTunes.
5. Select your Apple TV in the Devices list, and then click Restore.

(You may already have a micro USB cable if you have a camera or other digital device)

• Check that you have correctly followed the instructions for your model of Apple TV.
• If not already, try using a powered USB port.
• Repeat the process but this time try connecting the cable while iTunes is closed.
• Repeat the process with another cable.
• Try restoring the Apple TV on another computer in another location.