To put your question in context, it is important to realize that all vertebrates (including us) are descended from a bilaterially symmetric ancestor that lived more than 500 million years ago. 

- Pikaia was an early relative.

To be bilaterially symmetric means to have two sides, left and right.  These are nearly, but not quite, mirror images of one another. 

In bilaterially symmetric organisms, the digestive tract runs down the middle of the organism, from mouth to anus -- it is formed during the process of gastrulation.

During early embryonic development, molecular differences (due to differences in which gene are "expressed") emerge between the cells that compose the different regions of the embryo.  Specific groups of cells go on form various organs through process known as morphogenesis and differentiation

How specific organs form can be more complex than you might think.  Although we only have one heart, it actually forms from two seperate groups of cells, known as the cardiac crescent (the cells that connect them will form the outflow tracts of mature heart.)

On the other hand, the lungs originate as a single bud that emerges from early foregut, which gives rise to both the eosophagus and the trachea. . 

As this bud grows, it splits (bifurcates) and the two sides form the left and right lungs. 

The kidneys, like the cardiac crescent, forms as distinct structures, one on the right and the other on the left side of the body.   Unlike the heart, the two kidneys remain distinct.

In each case the form of specific organs in the adult is determined by functional adaptations, evolutionary history and constraints.

use the wikipedia for more information and definitions of words you are unsure of!