Excellent question. Basically chiral objects are non-superimposable mirror images. So for example, your left hand is a mirror image of your right hand, but it is impossible to superimpose the two. A sphere on the other hand, is achiral, because a ball can be superimposed on its mirror image.
In biology, almost all molecules used by living organisms are chiral, and of a particular handedness. Amino acids are almost always left handed, and sugars are almost always right handed. You can imagine that a protein composed of both left and right handed amino acids could have wildly varying shapes. Since a protein's structure is critical for its function, cells must tightly regulate the production of amino acids. Amino acid synthesis proteins will only catalyze the production of left handed amino acids.
Of course, this leads to a chicken-and-egg problem, which is what you alluded to in the OP. Which came first: left handed amino acids or left-handed amino acid synthesis proteins (which are themselves composed of left-handed amino acids)? Unfortunately, there is no firm answer yet, but there are some interesting hypotheses.
According to this
link, the presence of certain achiral molecules in a solution can actually catalyze the production of an enantiomeric excess of another molecule. Enantiomeric excess is just a measure of the relative proportions of left and right handed forms- the excess implies that more of one handedness is created than the other. Interestingly, the chemists who discovered this received the Nobel prize a few years back.
Where could these achiral molecules have come from originally? Well, one hypothesis is that they came to the earth from meteorites. Some meteorites have been found to contain an excess of left-handed amino acids. See
here for more information.