A regulator allows you removal of the gas from the cylinder via a controlled method, rather than just opening up the valve and letting all the gas escape at once. A two stage (having two dials for tank pressure and outlet pressure) is better than a single stage regulator.
Allows for the fine control of the gas exiting the tank via the regulator. Without a needle valve you would be using way too much gas for your tank. It allows control down to a bubble per several seconds. Most folks run their tanks in the 1-2 bubbles per second range. Your water hardness and tank size will play a part in this.
Related to the answer in the first question. The 'second gauge' of the regulator.
This gives you the ability to run multiple tanks from one CO2 source. Think of it as a 'T' or a 'gang valve' type of apparatus.
An electronic device which will turn on and off the gas flow. Lots of folks will only run the CO2 when their lights are on. If you have hard water, you will find this doesn't do anything for you, as you will probably need to run it 24/7.
Think of this as an 'o-ring' to create a good seal between the regulator and the tank.
HTH.