The terms are derived from the fact that some 90% of the population are right-handed, that is, favour their right hand for a variety of tasks. The direction right is a cognate of "right" meaning correct or good. The word "left" comes from the Old English lyft, meaning weak. This dichotomy can also be seen in the words "dextrous" and "sinister", from the Latin words for right and left.
In the vast majority of the population, the heart is slightly to the left of the body's centre line and the liver is to the right. Less visibly, the two hemispheres of the brain have different functions, with the left side specializing in logical thought and the right side in intuition.
Mirrors are said to reverse left and right. Strictly, this is not true: the image of your left hand is on your left-hand side. However, it is seen at the position corresponding to that of the right hand of a real person opposite to you. Thus one can say that the mirror has the combined effect of turning you around and reversing left and right. One can also say that it reverses front and back side. If you take a cube, write "left", "right", "top", "bottom", "front", "back", and hold it, so that all sides face the correct direction, then hold a mirror behind it, without moving the cube or yourself, you will notice that "front" and "back" are swapped in the mirror image, but the other sides are still correctly labelled.