or in some newbie language, the Arduino is working with 5V, while most common LEDs work with 2-3V - give it too much 'juice' and "kapow!"
Now, LED's are not voltage-driven components, so it's not correct to say, that they work with 2-3 volts.
LED's are always current-driven - the voltage drop across the LED depends on the chemistry inside it. It is usally around 2 volts for standard Red, green and yellow, and for blue & white, it's around 3.6 volts.
The current all depends on the kind of LED - standard junkbox LED's (indicator lights) can handle around 20 mA.
So if driving a standard red indicator LED from an Arduino-output, you would calculate the resistor like this:
5V (Arduino voltage) - 2V (LED Voltage drop) = 3 volts we need to "burn off" in a resistor.
3 / 0.02 (2 mAmps) = 150 ohms. If your calculation ends up with a value of resistor not in your parts bin, you take the next higher value. e.g. if your calculation says that you need a 130 ohm, you use a 150 ohm.