The basic structural and functional unit of the kidney. Consists of a renal corpuscle (with Bowman's capsule), a glomerulus, a proximal convoluted tubule, a loop of Henle, a distal convoluted tubule and drains into a collecting duct with a related vascular supply.
Each human kidney has about a million nephrons.
The basic function of the nephron is to regulate water and soluble substances (especially ions) in the body by filtering it all out first, reabsorbing what should be kept and excreting the rest. I cannot understate the importance of this.
A full writeup of the function of the nephron would take up several chapters of any good physiology or urology textbook so I'll try my best to sum it up in one sentence.
The nephron filters the blood, concentrating the filtrate, reabsorbing ions (sodium, potassium, calcium, hydrogen, bicarbonate, chloride, ammonium) and solutes (glucose, amino acids, phosphates, etc.)according to the body's needs, under hormonal control from anti-diuretic hormone, aldosterone, parathyroid hormone, atrial-natriuretic peptide and probably some others ... to create urine ... and, in so doing, eliminates wastes from the body, regulates blood volume and blood pressure, regulates the levels of important electrolytes and metabolites and regulates blood pH levels.