It is all about symmetry!
Chirality is a property of asymmetry of objects. The word chirality is derived from the Greek word χειρ (kheir), which means "hand".
An object (or a system) is chiral if it is not identical to its mirror image, that is, it cannot be superposed onto it. A chiral object and its mirror image are called enantiomorphs (Greek opposite forms) or, when referring to molecules, enantiomers. A non-chiral object is called achiral and can be superposed on its mirror image.
Human hands are perhaps the most universally recognized example of chirality in the real world. The left hand is a non-superimposable mirror image of the right hand; no matter how the two hands are oriented, it is impossible for all the major features of both hands to coincide.
In chemistry, chirality usually refers to molecules. A chiral molecule is a type of molecule that has a non-superposable mirror image. Achiral molecules are symmetrical, identical to their mirror image. These two mirror images of a chiral molecule are called enantiomers or optical isomers. Pairs of enantiomers are often designated as "right-" and "left-handed".
Nature is chiral
One may well think that both forms of chiral molecules ought to be equally common in nature. But when we study the molecules of the cells in close-up, it is evident that nature mainly uses one of the two enantiomers. That is why we have – and this applies to all living material, both vegetable and animal – amino acids, and therefore peptides, enzymes and other proteins, only of one of the mirror image forms. Carbohydrates and nucleic acids like DNA and RNA are other examples.
Thus the enzymes in our cells are chiral, as are other receptors that play an important part in cell machinery. This means that they prefer to bind to one of the enantiomers. In other words, the receptors are extremely selective; only one of the enantiomers fits the receptor's site like a key that fits a lock.
Since the two enantiomers of a chiral molecule often have totally different effects on cells, it is important to be able to produce each of the two forms pure. Chemistry brings us solutions to achieve this goal.
For more info, see also an interesting video "What is chirality and how did it get in my molecules?" at http://ed.ted.com/lessons/michael-evans-what-is-chirality-and-how-did-it-get-in-my-molecules