Importance of a current-limiting resistor in an LED circuit
LED is basically a forward-biased diode:
Like a revered biased zener, it has a fairly constant voltage drop of 1.5V to 3V.
If you supply more than this voltage, even slightly more, a large current will flow through it, as there is no mechanism to absorb the excess voltage (LED - supply). Result: LED damage from overcurrent.
Mechanism of current limiting resistor:
A resistor in series absorbs the voltage difference and sets a safe current through it.
A series resistor also has a secondary purpose of setting the light intensity of the LED. Especially in a battery powered gadgets, it is important to conserve battery.
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