LED stands for Light Emitting Diode. LEDs works similarly to other types of diodes, except that they emit light when current is passed through them.
Like other types of diodes, they allow current to flow in one direction but block current flow in the other direction.
When you apply a tiny voltage in the forward direction, at first hardly any current flows and nothing happens (no light). As you gradually increase the voltage, all of a sudden you reach the voltage where current flows and it is like a huge spigot. If you do not limit the current, it will burn up or blow up the LED, literally. This voltage where current will suddenly flow is called the forward voltage or forward voltage drop.
While regular diodes have a forward voltage drop of around 0.7 volts, and schottky diodes only around 0.4 volts, LEDs have a much higher forward voltage drop, typically around 2 to 2.2 volts.
Like regular diodes, LEDs will fail if you apply too much reverse voltage. They will block that reverse voltage up to a point, then they will fail, usually short but sometimes open.
Current limiting can be a simple resistor if you have a known, (relatively) constant voltage. This is fairly inefficient most of the time but is easy to figure out. You just use Ohm's Law to decide what size resistor to use. So let's say you want 20 milliamps (0.02 amps) to flow through your LED. In a 12 volt system, you will drop about 9.8 volts through the resistor (12 minus the 2.2 volt forward drop in the LED). So 9.8/0.02=490 Ohms. 470 Ohms is a standard size that is plenty close, so with a 470 ohm resistor we will get 9.8 volts divided by 470 ohms equals 20.8 milliamps.