Incandescent bulbs, as has been said elsewhere, work by getting a filament of tungsten wire hot enough to glow. This glow is across the entire spectrum, from infrared through visible light, and into ultra-violet. A lot of the energy pumped in gets released as energy which is invisible to us.
LEDs, on the other hand, release energy only in a very narrow and very specific frequency range. A red LED only emits red light. A green LED only emits green light, and so on. All of the energy gets released in the visible spectrum. Since there is no energy wasted on non-visible frequencies, we get more brightness for the same amount of energy.
The so called “white” LEDS are actually ultra-violet LEDs with a phosphorescent chemical that glows white when exposed to UV, or are a well chosen combination of red, green, and blue LEDs. Either way, their efficiency comes from the same source: not wasting power on useless parts of the EM spectrum.
As to how they work, an LED consists of P-Type and N-Type semiconductor material joined together at a junction. Electrons move through P-type material in a low energy state. Electrons move through N-Type material in a high energy state. When the electrons cross the junction, they move from a high energy state to a low energy state. When they do that, they give off a photon of light. Because the difference in the energy states is constant, the frequency of light is constant.
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