In acute renal failure, particularly acute tubolar necrosis, the tubules become blocked with cellular matter, particularly necrotic sloughing of dead cells. This debris obstructs the flow of filtrate, which results in reduced output of urine. The arterial supply of the nephron is linked to the filtration apparatus (glomerulus), and reduced perfusion leads to reduced blood flow; usually this is the result of pre-renal pathology.
The kidney's resorptive mechanisms are particularly energetic, using nearly 100% of the O2 supplied. Thus, the kidney is particularly sensitive to reduction in blood supply. This phenomenon occurs because renal flow is restored prior to the normal resorption function of the renal tubule. As you can see in the graph, urine flow recovers rapidly and subsequently overshoots the typical daily output (between 800 mL and 2L in most people). Since the kidney's resorption capacity takes longer to re-establish, there is a minor lag in function that follows recovery of flow.