An LED (Light Emitting Diode) emits light when an electric current passes through it. The simplest circuit to power an LED is a voltage source with a resistor and an LED in series. Such a resistor is often called a ballast resistor. The ballast resistor is used to limit the current through the LED and to prevent that it burns. If the voltage source is equal to the voltage drop of the LED, no resistor is required.  The resistance of the ballast resistor is easy to calculate with Ohm’s law and Kirchhoff’s circuit laws.

 

All LEDs require some form of current limiting. Connecting an LED directly to the power supply will burn it out immediately. Overdriving, even briefly, will significantly reduce it's life and light output.

Fortunately, driving a single or a string of low current (20-30 mA) LEDs is a simple task - adding a small resistor in series is the easiest and cheapest way to limit the current.

Keep in mind however, that high current (above a few hundreds of mA) LEDs are tougher to drive, and while they can be operated with a series resistor, to minimize power loss and ensure reliability, it's advisable to use a more expensive switching current regulator.

 
We should avoid connecting LEDs in parallel with just one resistor shared between them. Identical LEDs can be successfully connected in parallel, but each LED may have a slightly different voltage drop, and the brightness of the LEDs will differ. If you want to connect the LEDs in parallel each one should have its own resistor. Calculate the value for a single LED and connect all the LED-resistor pairs in parallel.