Knock sensors are just one of the things that separate the newest generation of internal combustion engine from the previous. The knock sensor is your computer's "ear" on the engine; while it is important in terms of optimization, your computer still won't quite end up flying blind without it.
A knock sensor is essentially a piezoelectric microphone, just like the pickups on an electric guitar. A piezoelectric, or PE, is a material that turns shock load or kinetic energy directly into electrical current. Applying mechanical pressure to a PE like lead zirconate crystal, bone, silk or even tooth enamel causes the substance's magnetic domains to rapidly align and re-align, which creates electricity. Sound energy affecting a PE sends a tremor of compression through it, which causes the PE to emit an electrical output of a certain voltage and frequency.
Engines make a lot of noise, and not just the powerful bangs associated with the combustion event. Subtler notes flow all through the engine block -- the sound of the crankshaft spinning, the percussive tap of the valve train and harmonic reverberations vibrating the block like a bell. The computer knows and recognizes most of these sounds, but sends up an alarm when it hears the sour note of fuel pre-igniting or detonating in the cylinder. The knock you hear from the driver seat is just the loudest of a range of subtle sound waves emitted by abnormal combustion.
Upon detecting knock, or any of the subtle vibrations that precede it, the computer adjusts engine timing and air/fuel ratio to get rid of it. Many modern engines are actually tuned to run right at the limit of knock to optimize engine power according to the fuel octane and altitude. In fact, the knock sensor is a vital tuning aid for "flex fuel" engines that may see fuels with an octane range from 84 through 112, from the poorest mule-urine-grade gas to highly refined ethanol.
Engineers don't expect your sensors to last forever, which is why they program the computer to self-diagnose most of its sensors. If the knock sensor fails or its readings go far out of range, the computer will likely switch to a default program that doesn't rely on input from the sensor. You're almost certainly going to lose power, but how much you lose depends on how close the computer runs the engine to its octane limit and how heavily it relies on knock sensor input.
Turbo-charged, high-compression and flex-fuel engines stand to lose the most power and may severely retard timing and keep the transmission out of overdrive until the knock sensor's been replaced. This, the dreaded "limp home" mode, is designed to make the car practically useless until you get the sensor fixed. Manufacturers do this intentionally because the default program produces higher emissions than the standard feedback program -- a no-no where the EPA is concerned.
