In JDH's answer, he discusses the phenomenon of orientability, in which a space 'has a concept of left handedness'- in truth it would be more acuurate to say *one can give the space a concept of left handedness*- for there is always a coice of two.

This could be said to correspond, at least in two dimensional cases like the sphere (although it does extend naturally) to whether one chooses the inside or outside of the surface to walk around. Imagine two ants walking between two given points (close enough there is an obvious shortest route) on a soccer ball, one on the outside, the other trapped inside- at each point 'outside ant's' right is 'inside ant's' left and vice versa. (incidentally, this gives a nice way of thinking about non-orientable surfaces as surfaces having only one side)

Now you'll notice that, as you were visualising the inside and outside ants walking between two points, you were able (perhaps with some difficulty) to identify what they would call left and right. This is because for each ant I implicitly gave you a definition of what forwards was, and what up was- and you could have used the superficially satisfying definition:

> Right is a quarter turn clockwise from forward, when viewed from above

Now this is only superficially satifying, as it rather leaves one wondering about how one defines 'clockwise'. In fact the two are tied up together- defining one will automatically give one a definition of the other, and sadly each is to all extents mathematically arbitrary (barring the aspect in which our mathematics emulates our physical world cf. the end of JDH's answer).

You see, the inside/outside correspondence I put forward toward the start of this answer secretly depends on the ants in question already having a left and right of their own that they bring to the table, so to speak. 

Where this comes from, then, is perhaps therefore the body and brain of the ant (or human!), in which the somatic, sensory and motor functions of each side of the body are lateralized to the opposite side of the brain (that is, for example, the left visual hemisphere is represented in the right visual cortex), so the brain **already knows** its left from its right **preverbally**, and from there it's just a matter of association with sounds and shapes to 'learn' left and right as we do.