At the most fundamental level, a digital output is like a light switch, as shown in the circuit diagram below (consisting of a 5V battery, a switch, LED light, and a 220 ohm resistor). If the switch is open, the light is in the off state. If the switch is closed, the light is in the on state.
However, the hardware of a simple switch is inflexible and cannot be changed without altering the physical circuit. That is why microcontrollers, like Arduino, are used for many devices, as they can perform a wide range of tasks through software changes, without changing the circuit itself. The diagram below shows such a circuit with an Arduino board:
And this shows what it looks like in real life, with the LED and 220-ohm resistor plugged into a breadboard:
Note that the positive (longer kinked) lead of the LED is connected through the short red wire to digital pin 3 on the Arduino, and the negative lead of the LED is connected through the resistor (and then through the black wire) to ground. The longer red wire at the top is connected to the 5V power pin on the Arduino.
The Arduino is then connected to the computer via a USB cable, as with the blue cable below (breadboard not shown):
Once the Arduino is connected to the computer via the USB cable, you should see a light on the board turn on, indicating it is getting power from the computer (assuming the computer is on).
The final step in establishing a connection between the Arduino and the computer is a software connection, using either "ChDuino" software (for Windows and Mac machines) or an "Arduino Controller" extension for Chromebooks. For details on the Windows/MacOS software, see https://roboblockly.com/u/1307.php. For details on the Chromebook software, see https://roboblockly.com/u/1322.php. The necessary software may be downloaded for free at www.barobo.com/downloads. Full instructions are also available at roboblockly.com/setup/arduino.