The condition of being
born with only one
kidney.
Unilateral renal agenesis occurs
approximately once in every
1,000 live births, tends to
affect more
males than
females, and most often results in a missing
left kidney.
Unilateral renal agenesis is generally not
diagnosed in
infancy because it tends not to produce
symptoms; instead, the lone
kidney grows in size to
compensate for the
deficit.
Nevertheless, this condition can
manifest itself in some more mundane ways, such as
hypertension or mild
hearing loss (since the
kidneys develop around the same
gestational time as the
ears).
According to the disturbing but extremely informative medical text The Developing Human: Clinically Oriented Embryology, unilateral renal agenesis occurs "when the metanephric diverticulum fails to develop or with early degeneration of this ureteric primordium." Since my wife was the one that went to medical school, I will leave this explanation as is and not clutter it with my weak interpretation.
Unilateral renal agenesis should be distinguished from a condition known as Horseshoe Kidney, where two distinct kidneys fuse together at either the superior or inferior poles.