What is the "on condition" concept of aircraft maintenance?
I'm not a maintenance guy, but you may be mixing 'inspection' and 'maintenance' together here.

An inspection helps you decide if maintenance is needed or not. For example, inspecting the tire tread before every flight, or checking the cylinder compressions every 100hrs. If the inspection shows that the condition of the item is still within acceptable limits, then you don't need any maintenance yet. This is the 'on condition' or 'condition-based' approach, at least as I understand it.

Another approach is to do planned maintenance at fixed time intervals whether it's 'necessary' or not. For example, replacing engine oil every 50hrs, or replacing the entire engine every 2000hrs. In this case it doesn't matter what the item's physical condition is, you perform the maintenance even if everything looks good.

FWIW, some people strongly prefer the 'on condition' approach, especially for piston engines (see this book, for example). But even they probably replace their oil at more or less fixed intervals.

If you want something more official, I found an FAA definition:


  On Condition Item (Oc)
  
  A primary maintenance process requiring repetitive inspection or test
  to determine the condition of units, systems or portions of structure
  to assure continued serviceability. Corrective action is taken when
  required by item condition as determined by analysis of inspection
  and/or test results.


The key point as I understand it is that you base the decision to do maintenance (or not) on the physical condition of the item.