A left and right hand are mirror images of one another. Unlike a ball and its mirror image, a hand and its mirror image are not identical. In the unlikely event that you doubt this, try fitting a left handed glove onto your right hand!
An object such as a hand that is not identical to its mirror image is chiral. An object such as a sphere which is identical to its mirror image is achiral. The word chiral derives from the Greek word for hand.
Pasteur saw that optical activity was a property of the molecules of tartaric acid. However, it was not until 25 years later that two scientists, J.H. van't Hoff and J. A. LeBel simultaneously but independently provided the explanation. They knew that there are two different ways in which four different objects can be arranged at the corners of a tetrahedron, and that the two arrangements are mirror images of one another. Van't Hoff and LeBel proposed that carbon has a tetrahedral structure, and that optically active substances have at least one carbon atom with four different groups attached. The "+" and "-" forms of tartaric acid therefore corresponded to molecules containing two mirror image tetrahedral structures, each centred on a carbon atom.
It is worth noting that Van't Hoff and LeBel made their proposal at a time when very little was known about the structure of atoms or chemical bonds. It was initially controversial, but soon came to be generally accepted and is now regarded as fact.
The key point to note is that the two mirror image molecules are not identical. In particular, it is not possible to superimpose one molecule on the other. To see this, imagine moving the right hand molecule to the left so that the black, yellow and blue parts of each of the two molecules line up. The red and green parts will not line up, and there is no way to make them do so without physically breaking and re-making the bonds of one of the molecules. The molecules are therefore chiral.
Now imagine replacing the red spheres with green spheres, so that each molecule now has two green parts. It is now possible to move the right hand molecule to the left so that all of its parts line up with the corresponding parts on the left hand molecule. In this case, we can see that the two mirror image molecules are identical, and therefore achiral.
Given that most objects around us are chiral, it comes as no surprise that the same is also true of molecules, including those from which organic lifeforms are constructed. The simple fact is that there are vastly more ways of putting atoms together in a way that produces chiral molecules than there are ways of putting them together to make achiral molecules.
It is however noteworthy that many of the key macro-molecules of life are constructed from chiral sub-units which are linked together in such a way that all the sub-units are of the same chirality.
The "+" and "-" forms of chiral molecules are known as dextrorotatory ("+" form) and levorotatory ("-" form). Dextrorotatory molecules rotate polarised light in a clockwise direction. In the case of levorotatory molecules, the direction of rotation is anti-clockwise.
All protein molecules in all contemporary species, from bacteria to humans, are constructed from the same set of 20 amino acids. With the exception of glycine, which has a symmetric structure and is therefore achiral, all amino acid molecules are chiral; they can exist in two mirror image forms. However, in proteins they exist only in their levorotatory form. A similar point applies to other important biological macro-molecules including DNA; they are constructed from sub-units of uniform chirality. Such macro-molecules are described as homochiral.
The homochirality of biological macro-molecules such as DNA and proteins can be understood as a necessity for contemporary life-forms. Structure is crucial to the correct functioning of both DNA and proteins. Were a molecule of 'DNA' to be constructed from sub-units of different chirality, it would not correctly form the familiar double helix structure. A similar point can be made about proteins. These macro-molecules perform an enormous range of functions in living organisms, and in most (if not all) cases the physical shape of the protein plays a key role in determining its function. If a particular protein molecule is always constructed from amino acids of uniform chirality, then the polypeptide string formed by the amino acids will always fold in the same way so that the protein molecule formed will always have the same shape. If amino acids of randomly mixed chirality were used, then the resulting polypeptide string would hardly ever fold into the same shape, with the result that most of the 'protein' molecules formed would not be able to function effectively.