Velcro is a trademarked 'hook and loop' fastener. It works by pressing both sides of the fastener together. One side is composed of small hooks, and the is composed of small loops. When pressed together the hooks tend to snare the loops and attachment occurs. Velcro is most commonly made of nylon and/or polyester. Depending on how well the hooks are ensnared in the loops a single square inch of velcro can hold up to 90lbs.
Velcro is used any time two things need to be temporarily fastened together. For normal use it is seen in shoes, jackets, and gloves. However there are much more exotic uses of Velcro as well. NASA uses velcro in space for many different applications. For example the astronaut space suits are fastened with velcro. Also, when sitting down the astronauts attach themselves to the chair with velcro.
A research group in Korea is attempting to make a nano sized equivalent to velcro. They have produced and published a paper called Shape-Tunable Polymer Nanofibrillar Structures by Oblique Electron Beam Irradiation that discusses their research.