The bandgap sets the color
An LED is a PN junction where forward current makes electrons and holes recombine directly at the junction instead of just diffusing across it. Each recombination releases its energy as a photon, and the photon's energy — its color — is fixed by the semiconductor's bandgap, not by a dye or filter. That is also why the forward voltage jumps by material family rather than sliding smoothly with wavelength: red, orange and yellow LEDs use AlGaInP or GaAsP with a roughly 2 V bandgap, while green, blue and phosphor-converted white LEDs use InGaN, whose wider bandgap needs over 3 V before it conducts at all.
Why every LED needs a series resistor
Past the turn-on knee, current rises so steeply with voltage that a fraction of a volt can mean the difference between a dim glow and a burnt-out die. An incandescent bulb is self-limiting because its filament resistance climbs as it heats; a diode junction does the opposite, so nothing internal stops the current from running away. In practice only the bulk and lead resistance inside the package holds it back at all, and that alone is not enough — which is why every real circuit feeds an LED through a series resistor, or a proper constant-current driver, and never straight from a voltage source.
Reading the datasheet
LED datasheets specify forward voltage at a stated test current rather than a saturation current, together with luminous intensity in millicandela or flux in lumens, a viewing angle, and a maximum forward current the die can dissipate without failing. Push current well past that rating and light output does not keep pace — efficiency droop means each extra milliamp buys proportionally less brightness, and heat pulls the output down further still. The reverse voltage rating is also unusually low compared with a rectifier diode, since an LED's junction was never designed to block a high reverse field.
Where it is used
LEDs serve as indicator lights, segments in seven-segment and dot-matrix displays, and backlighting in nearly every screen. Blue LEDs coated with a yellow phosphor produce white light efficiently enough to have displaced incandescent and fluorescent bulbs in general lighting, and infrared LEDs drive remote controls and optocouplers. Above a handful of LEDs, a single resistor is usually replaced by a dedicated constant-current driver IC, which regulates brightness far more precisely and efficiently than a resistor ever could.