A Ghost Box or Frank's Box is essentially a scanning radio receiver that cycles through the radio spectrum picking up snatches of broadcast signals and static (note that they typically lock on to broadcast carrier signals, and hence are likely to pick up a coherent snatch of a given wavelength before moving on). There are typically knobs and switches to adjust the frequency range, cycling speed, volume, etc., to achieve the most convincing outcome for the credulous user.

The concept was invented by Frank Sumption who makes a number of preposterous claims about the box's abilities while simultaneously saying it's not paranormal. Frank Sumption clearly shows his contempt for a scientific or even coherent view of the real world when he is quoted as saying:

There is no objective hard physical truth or universe. We all create what we want to see, and everyone thinks their truth supersedes everyone else’s truth.

Despite this apparent origin, Thomas Edison made a couple of published references to a device he was either considering (likely) or prototyping (unlikely) that would be a communication mechanism with "...another existence or sphere", and these references have been used by some to claim it was Edison who was the originator of the ghost box. It does not seem, however, that Edison's device was ever completed or demonstrated, and likely never got beyond the conceptual stage.

The device "works" due to the principal of pareidolia, essentially the tendency to see significance or patterns in random stimuli, in this case radio transmission snatches and static. You can see from the "Hi" example video presented here how the questioner presents a question with the device off (conveniently avoiding any appropriate "responses" that might be heard even before the question is asked), then switches it on and cherry-picks fragments from the sound to suit a response he needs. In this case, like "psychically" cold-reading a person or working with EVPs, the question presented is broad in potential responses so that it's not surprising when some sounds appear that can be viewed by the gullible as supernatural conversation. Similarly this video shows a user (this time with the device on continuously) asking questions, then waiting whatever length of time is necessary to get something that the user feels is a response, regardless of how apparently unrelated the "response" is to an objective observer or how many other noises and snatches of wording occur before or after.

In short, the device is simply a pseudo-random noise generator, and misleadingly uses actual coherent sound as the raw material from which the noise is generated. The interpretation by the user is then used to bolster or expand their own particular brand of fantasy as needed.

For more opinions, there is a post on the JREF site inviting responses that has a number of skeptical perspectives to peruse.