In scenes with many reflective and transparent surfaces, POV-Ray can get bogged down tracing multiple reflections and refractions that contribute very little to the color of a particular pixel. The program uses a system called Adaptive Depth Control (ADC) to stop computing additional reflected or refracted rays when their contribution is insignificant.
You may use the global setting adc_bailout keyword followed by float value to specify the point at which a ray's contribution is considered insignificant. For example:
global_settings { adc_bailout 0.01 }
The default value is 1/255, or approximately 0.0039, since a change smaller than that could not be visible in a 24 bit image. Generally this setting is perfectly adequate and should be left alone. Setting adc_bailout to 0 will disable ADC, relying completely on max_trace_level to set an upper limit on the number of rays spawned.
See section "Max_Trace_Level" for details on how ADC and max_trace_level interact.