I2C is a generic and widely used digital communication protocol for "simple electronics" -
http://en.wikipedia.org/wiki/I%C2%B2C It is commonly used to allow a microprocessor to talk to a bunch of simple devices such as memory, sensors, ADCs or intelligent batteries. Check out the Wikipedia link for more examples, my list is by no means exhaustive.
NXT uses I2C to talk to some of its sensors. The DSC provides support to talk to those same sensors. Be careful though, not all NXT sensors use I2C. I2C sensors are also available from many other sources.
I2C allows a processor to use 2 pins to talk to many devices. If you are interested in electronics, I'd recommend looking into how it does this - it is a very cheap but decent method.
The new system also supports SPI, which is a digital communication protocol that competes in the same niche of "super simple for simple tasks". I'm excited to see what teams will end up doing with these two buses.