Sampling is taking sections of audio from a range of tracks and playing them back in a new order to create something totally new. It originates from the early use (and is still today) in hip-hop.
Samples can be ordered, processed and mixed with a DAW (digital audio workstation). Alternatively, individual samples or one single sample can be assigned to notes on a keyboard or pads on a sampler to be triggered live. Here’s a great example of live sampling in use:

This video shows the use of a Novation Launchpad. An 8×8 button controller, each can be assigned a sample or keys of an instrument. The Launchpad is used here along with Ableton Live, which is a great DAW (digital work station) commonly used when live sampling. It allows the user to have full control over what samples they use, time stretching, warping and pitch adjustments.