copper coiled sheets of steel
Sounds like you have a fluorescent table lamp.
You might like to read about these here:
http://en.wikipedia.org/wiki/Fluorescent_lamp
The "copper coiled sheets of steel" thing is called a ballast and it is a type of inductor.
A current is passed through this and then switched off. This is done by the "starter" which looks like a small plastic cylinder.
This generates a large voltage from the ballast, which makes the lamp draw current and light up.
After that, the current in the lamp is limited by the inductance of the ballast so that the lamp does not get too hot.
So, the ballast performs two functions.
You use an adaptor when the device you want to power uses a different voltage to the mains supply or when the device needs a DC (direct current) supply.
Usually the DC supply will also be at a lower voltage than the the mains supply as well as DC.