Active noise cancellation is the technology described above, where microphones and speakers work together to reduce or remove background noises. It was originally only found in larger over-the ear headphones that could contain the hardware required for the technology , but never models have made it possible for active noise-cancelling technology to be built into in-ear headphones.
Passive noise cancelling works differently.This uses specially designed hardware such as ear cups and seals to simply seal out the background noise. A little like earmuffs, this essentially inhibits the sound waves from reaching your eardrums. It is not usually as effective as active noise cancellation but certainly has its benefits.