It is the same principle that works in chemistry. The different mirror images of a chiral molecule will produce different products when reacted with only one mirror image of another chiral molecule. These differences may show up in solubility, which can be exploited by chemists to separate the left and right-handed forms of the molecule. In biology, chirality takes on even more importance. Specific proteins called enzymes mediate most biochemical reactions.
Enzymes are very specific to the reaction that they mediate.
The chemicals at the start of the reaction fit into the enzyme like a 3-D key into a lock. Not too surprisingly, the mirror image molecule often isn't acceptable - it just doesn't fit the lock. In nature, many chiral molecules such as sugars and amino acids are only present as either right or left handed molecules, and not a mixture of both. Organisms have evolved to only recognise one form. The consequences of having the wrong-handed molecule can be dire.