Diodes are parts which let current pass only in one direction - like unidirectional valves for air in bicycle tires they act on currents. Current flow in one direction is permitted, flow in opposite direction is blocked.
The voltage which is given for a diode is in most cases the maximum allowed voltage which is blocked. So like for an air valve which can stand 10 bars of pressure a diode can for example withstand a voltage of 100V. If the voltage is further increased the diode will break (and current will flow). This voltage is called the "break down" voltage. Note: the voltage ratings given by manufacturers aren't the breakdown voltage - they usually only label the allowed maximum voltages!
The current flowing through a diode in the conducting direction is called the forward current. It is a maximum rating which is usually meant for permanent use. Depending on the model, higher peaks of current are no problem for a diode. If used for too long the diode will heat up and burn. Have a look at the example for the 1N4148 Diode on wikipedia.
Zener Diodes
There are specially designed diodes called zener diodes where the breakdown voltage is set to a very precise point - for example let's assume at 4.7 V.
If used with only 3V the zener diode will act as a normal diode. In forward direction it will conduct like every standard diode and let current pass. In opposite direction it will block current as expected for a diode.
If the voltage is now increased to slightly above 4.7 V the diode will again behave like a usual diode in forward direction. However in its usually current blocking direction it becomes conducting! Combined with an LED and a resistor in series you could use this for example as a very basic voltage monitor.
Standard Diodes - main differences apart voltage and current
Widely used types are the already mentioned 1N4148 and the 1N4007. They differ in their maximum allowed forward currents and also on their allowed reverse voltage (see the manufacturer's datasheet for details) and also in their switching "speed": Several diodes are comparably slow when getting from blocking direction to conducting direction. There are tasks where speed is important. The 1N4007 is a pretty slow diode - fast enough for most purposes - however in cases where a fast diode is required you should better use a "schottky" or "ultra fast" diode.
common use
- rectification of AC currents
- protection of circuits against reversed voltage
- fly-back diode protecting from short peaks on coils