In basic terms -"oxygen clean" means that the equipment (tank or whatever) is cleaned to a standard which minimises the risk of a spontaneous explosion (aka deflagration - an uncontrollable fire) due to gas under high pressure impacting materials or particles in the system which present a risk of combustion.
The act of compressing gas heats the gas - and vice versa - decompressing gas cools the system down (the term is diabatic de/compression). High pressure 02 cannot combust by itself but it provides a vector for combustion, and under pressure generates a great deal of heat - heat + 02 + combustible material = fire
Firstly - the materials used in a tank which is required to hold pure 02 must be "compatible" with high pressure 02 - i.e., material produced without the use of petrochemicals or other ignitable compounds - viton and teflon being brand names we hear (viton o-rings, teflon lined tubes) - even these will burn at very high temperatures, but significantly reduce the risk of fire over your ordinary o-ring.
O2 clean means removing any trace elements of hydrocarbons and other materials (even the grease from a human fingerprint), which might ignite in a high pressure 02 environment.
When it comes to the quality of the air being put into a nitrox tank, there are international standards for "breathable" gas which limit the amount of hydrocarbons or other pollutants in the gas to a level that is safe for human consumption. Hence the need for a filtration system on the air compressor used to pump your tanks. Beyond health concerns, "02 clean air" must be filtered to a point where the risk of unburned hydrocarbons is reduced to a level which minimises the risk of these particles spontaneously igniting in a high pressure 02 environment.
As previously mentioned - partial pressure filling means that a tank is pumped with pure 02 then topped up with air - in which case the system must be both 02 compatible and 02 clean. With bank (premixed) or membrane filling, the mixture pumped into the tank (say 32%) is highly unlikely to be rich enough to combust. As you will learn in the nitrox course, anything 40% or below is treated as regular air when it comes to safety concerns, and anything over 40% is treated as pure 02.
So - if you fill an 02-clean/compatible tank with air from a regular compressor that does not have the extra filtration system in place, you make the tank "unclean". If you use "02 clean/compatible" filtered 21% air, it's not a problem.
The actual partial pressure of a gas underwater after the tank is filled is immaterial - it's the filling process that is the main hazard.
Hope that answers a few questions.
Cheers
C.
PS - nitrox at my dive centre is free, free, free!