According to websters, regulation is, "The ability of a power supply to maintain an output voltage within a specified tolerance as referenced to changing conditions of input voltage and/or load."
If you graph the light intensity over time, this produces a "runtime graph". A light that is not regulated will produce a runtime graph that mirrors the discharge of the battery.
Different chemistries of battery ( or "Cell") have different discharge graphs. For example, alkaline tend to loose voltage quickly but then hang on for a long time. Lithium and NiMH tend to hold most of their power for as long as possible and then quickly die off.
Regulation is a feature whereby the flashlight output can overcome the tendancy of the battery - at least for awhile. Perfect regulation maintains a constant light output and then shuts off when the battery can no longer provide enough energey to maintain the constant output.
To regulate for a reasonable period, the battery must have more power available than the regulated level required. This "overhead" helps compensate for the gradual drop in battery voltage.
Incandescent lights have a self-regulating effect. As the battery voltage drops, the filiment wants to cool down but this reduces resistance which increase the current consumption. Said in another way, as the battery dies, the bulb demands more current. Of course, this is not completely linear, the effect is more noticable towards the end of the battery life, especially with alkaline.
LEDs on the other hand, quickly reduce their current consumption as the battery dies. This causes long tails on the discharge graph. In effect it is "negative regulation". LED as a result especially benefit from some form of regulation.
Many LED lights are direct drive or have a series resistor. The direct drive units rely on the internal resistance of the battery to limit current to the LED. This produces no regulation effect but is there to protect the LED from over current.
The advantages to regulation are that the light is brighter during the life of the battery (that life is reduced of course) and the battery is more completely used when it is replaced.
There are several types of regulation including voltage, current, light output, power, thermal, etc.
Peter
