Edison is a headless Linux device that comes on a board that is slightly larger than an SD Card.

On the card is

• 1 Phone SOC (with video and audio disabled),
• 1 GB LPDDR3 memory,
• Wi-Fi a/b/g/n  
• Bluetooth LE 2.1 + HDR
• 4GB eMMC storage
• Power Control Module
• Wi-Fi and Bluetooth Antenna
• Micro connector for a Wi-Fi Bluetooth antenna
• 70 pin I/O connector:
  • 13 pins for power
  • 4 pins for USB2.0
  • 9 GPIO
  • 4 GPIO w/PWM
  • 4 pins for 2 seperate I2C busses
  • 4 pins for I2S bus
  • 2 pins for UART2
  • 5 pins for SPI 
  • 4 pins for UART1
  • 8 pins for SD Card
  • 9 MISC pins
  • 4 unused

So with just a power source, you can connect to this device and start controlling it from a Linux console. 

You can design a board which you can connect your Edison to. Or you can use one of the already developed Edison boards. 

Currently you can use Edison as a Linux device, or as an Arduino Device (if you have the Arduino breakout board).  More operating systems will be enabled in the future.