I was reading about diodes and it says zener diodes can be used to voltage regulation. I read voltage regulation is used to provide constant voltage.

In DC currents theres a constant voltage anyway isn't there?

 

Most DC voltage sources will have varying outputs depending on load current and source stability, so regulation is used for the more sensitive circuits. Sometimes you may also wish to use a lower voltage (like 5 volts) but the only source is higher (say 12 volts) so a quick solution is to use a 5 volt regulator to derive this from the 12 volt source.

 

What does the load current mean?

 

It is the current that passes through the load.

 

for a power supply if the input supply changes the output magnitude also varies.
hence to maintain constant output regulation is required.

 

A zener can be used to regulate voltage but only for very small currents and they are not very efficient. You can use a zener and a transistor to get slightly higher currents but without careful design they can be unstable. Most designers use linear regulators that have all of the hard issues worked out. Find out the DC voltage and maximum current you need. Then you can find a 'three terminal regulator" to fit that specification. The most common ones are +5 http://www.national.com/pf/LM/LM78M05.html
+12
http://www.national.com/pf/LM/LM78M12.html

They are easy to use, apply up to the max allowed voltage to the in, ground to ground and the output will be fixed to the rated voltage.
Support parts can be added. Two filter capacitors one at the in and out and two diodes for short protection.
These work up to 500ma, a heat sink should be used even though the device has thermal shutdown.
If you need less current there are cheaper version of the part in smaller packages. You can get them so small it's almost impossible to pick them up!