Chirality n. (Kie-ral'-it-ee) The state or quality of being chiral, almost always in reference to molecules.

Basically, chirality is when a three dimensional structure's mirror image is structurally different than the original.
While refering to molecules, it is important to note that molecules can twist and rotate freely at certain points in their structure, which increases the range of what may be considered structurally equivalent.

Water lacks chirality. Even though sucrose is often shown in structural diagrams with the OH groups all on one side, the natural twisting and turning that occurs makes the mirror image equivalent.

Thalidomide is chiral. This is because, like all ethers and other ether-contaning molecules, it has a double bond (only single covalent bonds rotate freely) in its 'middle'. Both structurally differing forms are generated during the manufacture of thalidomide. While one form is fairly benign to humans when taken in controlled doses, it's mirror image is very harmful to the developmental processes of fetuses. (cf. children of thalidomide)
There is currently no clear or simple way of seperating one version from the other.

Apperently, 'Chirality' is also the name of a manga that Satoshi Urushihara is known for working on.
Additionally, 'Chirality' is not an polished, addictive Pipe Dream/Tetris-type game for the Macintosh put out by Ambrosia Software - you're thinking of 'Chiral'.