Dictionary Definition: 

“Asymmetric in such a way that the structure and its mirror image are not superimposable.”

Selected from OxfordDictionaries.com

Functional Definition: 

Chirality is an orientational property of some molecules.  Chirality is the idea that a molecule with a central atom and 4 attached molecules or elements cannot be superimposed on its mirror image. This characteristic is also called handednes. Think of the molecule and its mirror as your hands or the hands of a classmate. When the hands are flat-together each finger or attached molecule is the same. However if you flatten those hands out on your desk and try to put one on top of the other you notice that  the fingers don’t line up. Your thumb is by your pinkie and visa versa.  The same is said for chiral molecules.  No matter how you rotate them about their central axis they will never match up with their mirror.  In the case of chemistry chiral molecules do not overlay their enantiomers (optical isomers). In nature most biological molecules are chiral.

The figure bellow gives you a visual of the handedness explanation.

Figure courtesy of Perhelion of Wikipedia Commons