"narrowband" O2 sensors only respond in a limited A/F range, and have a delay - the computer averages the high and low voltages from the sensor to determine lean or rich. Inexpensive.
wideband O2 sensors have a greater A/F range to which they respond, and they don't suffer from the delay, so you can essentially read the A/F directly rather than having to average them. Expensive.
Try this to start:
Oxygen sensor - Wikipedia, the free encyclopedia