Unless you happen to live in a remote, isolated environment, you're always surrounded by all kinds of noise.
Noise is just sound that is too loud or not useful, such as the roar of engines or clanking of machinery. Noise cancellation technology tries to cancel or minimize unwanted sound. Sometimes, ear plugs and sound dampeners aren't convenient or efficient. Noise cancellation, in contrast, tries to block the unwanted sound at its source rather than trying to prevent it from entering our ears.
Sounds travel through the air as waves, and each wave has a specific shape, or "waveform." If you add two wave together that are going in the same direction, and the peaks and valleys of those waves line up, they are "in phase." This will double the volume of the sound. If you add two waves together that are going in the same direction, but the peaks of one line up with the valleys of the other, they are "out of phase," and will cancel each other out. Imagine a "positive" sound and a "negative" sound created at the same time. The two sounds will cancel each other out.
Digital signal processing (DSP) is the science of using computers to understand various types of data transmitted by signals: light from space probes, electrical voltages generated by the heart and brain, seismic vibrations, and radar and sonar echoes, to name a few. Most cell phones, CD players and hearing aids now contain one or more DSP devices. A digital signal processor determines which sound wave is required to cancel the unwanted sound wave, and it then creates that sound and amplifies it through speakers or headphones. The result is near silence.