As far as I remember, it's a method of transmitting data over very simple data lines, like one wire for data, one for clock and maybe two more for gnd and such.

The bandwidth and/or reliablity is very limited, the ranges are average, but simplicity of the device and low cost make it a medium of choice for applications like "smart homes" i.e. sensors scattered all over the house that turn lights on when someone enters a room, regulate the temperature etc. There are several microcontrollers which have bit-banging UARTs built in. The ADuC812 I have right in front of me is one - it supports 2 bit-banging protocols: I2C and SPI. Most PCs support it too - because it's the basic transport for sensors like CPU temperature, fan speed and such - so they just provide an extra header so you can plug into the I2C bus and use your userspace software to communicate with all devices on the bus - read the fans speed, check the CPU temperature or drive any device you have attached to the output header.

Pick a particular microcontroller for your application, then check its app notes, usually they describe the protocol and provide program examples as well.