Ummmm... I'm not sure where to start?! Please excuse me if some of the following is too basic for you...
The cylinder head ('head') is the casting (usually aluminium) that bolts onto the engine block. It seals off the cylinder bores, by means of a head gasket (which sometimes fails due to overheating/warping of the head). The head gasket has to be replaced whenever the head is removed, and it is a good idea to replace the bolts too on modern engines because the bolts are designed to stretch during tightening.
As you probably know, the head also has valves to let in the fuel/air mixture and let out the exhaust gases. These valves are operated by the camshaft which is usually mounted on or in the head for car engines since the '70s-'80s. So, the camshaft drive (usually a toothed belt) also has to be removed before the head can come off.
The cylinder head usually needs to be removed these days to repair the head gasket or to replace bent valves (being the aftermath of a camshaft drivebelt breakage).
In the olden days (the '60s and before) the cylinder head used to be removed quite regularly (50,000 miles?) for a 'decoke' and valve grind (the inferior quality of petrol and oils used to give a heavy carbon buildup that impeded efficient combustion, and engine valves and seats were made of a less durable material that could become pitted and not seal correctly).
Apart from these 'repair' operations, other cylinder head work is sometimes done to enhance engine performance:
'Planing' the head removes material from the surface that meets the block, bringing the combustion chambers closer to the pistons and thereby increasing the compression ratio. More compression = more bang = more power.
Enlarging the valves allows the fuel/air and exhaust to flow more freely. More fuel/air = more bang, etc.
Enlarging or smoothing the ports that feed the valves removes various imperfections left by the manufacturing (casting) process. Larger, smoother ports = more fuel/air... although in some cases the smooth low-speed running can be compromised if the port diameter is too large.
It is important to note that all this work is not free (fitting larger valves is particularly expensive) and in many cases, a transplant to a larger engine (or a turbocharged engine) will provide more power for less money.
In my personal opinion, there is not a lot of point modifying the FIAT FIRE engine cylinder head. Being a modern crossflow design, it is already capable (I think) of more flow than the (very de-tuned) camshaft profile can allow for (that is, the valves are not open long enough to allow very much mixture in/out). I think you would modify the cylinder head once you have larger carburettors/fuel injection, manifold, and a 'performance' camshaft. How many of these things does your friend with the Nova have?
Hope this helps... also do a few archive searches for smokeme's turbocharged FIRE conversions...
To return to your original question, a long time in the past people used to take the head off the 1116cc FIAT 128 engine (the same engine is used in the 1984-89 FIAT Uno 55/60) and fit it to the 1290cc engine of the FIAT 128 Coupe. This was a cheap performance tweak because the smaller combustion chambers of the head from the smaller engine gave a higher compression ratio when fitted to the larger engine. Maybe this is what your friend with the Nova did? I don't think the same trick would work with the 1301cc Uno engine, because I think the head is already the same as the 1116cc engine and the pistons are a different shape instead. Though, I could be wrong. And anyway, this has got nothing to do with the FIRE engine. I just mentioned it because it was the one time I could remember where 'changing the head' made a difference!
Cheers,
-Alex