To begin with, there are several types of olive oil, each determined by the method of processing.
Virgin olive oil is produced only by physical means, rather than by chemical treatment. The best stuff comes from only ripe olives (as green and overripe olives produce bitter and rancid oil, respectively) ground into a paste using millstones or steel drums. By definition, a virgin olive oil has not undergone any processing other than washing, decanting, centrifuging, and filtering (although none of these are required for virgin oil, nothing else is permitted). Some heat can be applied and, as long as it doesn’t alter the composition of the oil, the process can still be dubbed virgin pressing.
Refined olive oil is poor quality (either due to acid content or other defects) virgin oil that must be refined if it is to be edible. Refining is usually done with charcoal filters or chemical processes. Refined olive oil is more shelf-stable, but it’s also essentially flavorless.