To put it easy, LED brightness depends on the voltage they get. Typically, red LEDs take 1.7-2.2V. The higher the voltage across the LED, the brighter they are. Depending on how many LEDs you have in series, depends on what the voltage will be on each LED.
For example, you have an LED brake light. When the bike is on and the brake light is dim, there is resistor that reduces each LED to a voltage of 1.8V. When you hit your brake light, a new circuit introduces a voltage that is not lowered by a resistor which makes a 2.0-2.1V across each LED making them significantly brighter.