I have never fully understood these and would appreciate some clarification...

Obviously you are required to already have a previous Windows operating system, but installed or not?

What else is there to this?

Just curious.

From a legal standpoint, you are to have to have a eligable source operating system installed for the upgrade to work. Also the upgrade licence takes any caveats of the original licence with it, and makes the original licence null and void.
e.g. if you bought vista update and had a xp install with a "student only, you must uninstall when you leave school" clause on it, that vista upgrade takes on that clause, and also you are not allowed to install that xp again.

From a functional standpoint, the installer doesnt give a crap what you upgrade to, so especially Vista/7 there are very simple ways to get around all this (by using keyless installs, etc.) to install wholely on an upgrade key. The legality of this... probabily not allowed, but in code go right ahead.