Gary,
I'm not sure that a (necessarily) dumbed down description of the OBi would do much good. For example, you could explain to someone in a few minutes, the basics of how an automobile works, which might be useful if he were afraid of cars, or just curious. However, that brief outline would be insufficient for him to evaluate the advantages of one design over another. It's the same with VoIP -- in the simple view, OBi, Ooma and Vonage all look the same! (MagicJack and Skype would be different, only in that most of the work is done in the user's PC, rather than dedicated hardware.) Anyhow, here goes:
The call setup and teardown "signaling" is separate from the voice path. When you take the phone off the hook, the OBi notices the current flow and provides dial tone. It decodes the DTMF (touch tones) and sends the number dialed, along with (previously configured) user account information to a Google server. If the request is valid, Google contacts an interexchange carrier (IXC), e.g. AT&T or
Bandwidth.com, who initiates a call on the PSTN. If successful, a signal is sent back via Google to the OBi, which plays ringback tone to the user. When the call is answered, the Google server sends info to the OBi, giving the IP address and port of a server to receive voice packets.
The OBi converts the analog voice signal from the user's phone to digital samples, taken 8000 times per second. Each sample is encoded into eight bits. Each 20 milliseconds of voice (160 samples) is sent over the Internet in an IP packet to a Google server, which forwards it to the IXC server. For each packet, the IXC sends 160 samples over the traditional TDM (time division multiplex) telephone network, which routes it to the called party's central office. There, the samples are converted back to analog and sent over a copper pair to the destination phone, which reproduces the caller's voice. The entire process also operates in reverse, providing a speech path back to the caller.