Extra Virgin Olive Oil is the highest quality. It is always cold-pressed which means that the olives are milled and pressed mechanically right after harvest, without any heat or chemicals applied. Acidity must be under 0.8%.
'First cold pressed' on the label means that it is 100% extra virgin olive oil, not heat processed or chemically extracted. All extra virgin olive oil is first cold pressed.
Historically, when olive pulp was pressed on esparto grass mats under a heavy stone, the first pressing was the finest quality; subsequent pressings entailed adding hot water to extract the less pure oil. Today olive oil is extracted using high-tech centrifuges and there is technically no "pressing" happening at all. But the term "first cold pressed" is used for the very first extraction.
The acidity level of extra virgin olive oil is never higher than 0.8% (3/4 gram fatty acid per 100 grams of oil). This refers to the proportion of oleic acid, a monounsaturated fatty acid in the oil. The lower the acidity, the finer the oil. Most of our olive oils are under 0.2% acidity.
'Unfiltered' means that filtering of the olive oil is held to a minimum. Minute particles of olive will remain thereby enhancing the flavor of the oil. After a time they may settle to the bottom of the bottle. Of course, all olive oil is filtered to some extent to remove unwanted residue such as leaf fragments.
'Pure' olive oil is refined from olives of high acidity, perhaps because they dropped from the tree and burst open on the ground, or stored too long before pressing. All the impurities are removed chemically - along with its flavor. They then add some extra virgin oil to give it some taste. This cheaper oil is only suitable for frying. Sometimes this is just labelled as simply 'olive oil'.
Virgin olive oil has a much higher acidity than extra virgin olive oil. This means it has an unpleasant flavor and is best used for cooking.
'Light' olive oil is code for an oil that is highly filtered, removing much of the flavor and benefits of real extra virgin olive oil.
'Wild' oil is produced by trees, often hundreds of years old, which over the years have gone out of production. People are now returning to these historic groves to pick these organic, all natural olives.
'D.O.' followed by the name of a town or region, appears on the labels of some unique olive oils such as Señorío de Vizcántar, D.O. Priego de Córdoba or Unió, D.O. Siurana. This is an official government controlled designation to assure you that the product is authentic: the raw olives have to be grown within a specific geographical area; the distinctive qualities and characteristics are due mainly to the natural environment; and the manufacture of the product follows strict guidelines.
France has a similar system which assures you that a bottle of wine designated 'Chateau Yquem' is really from the village of Yquem; or that Roquefort cheese comes from that area and the cheese is formed in the traditional way; or that Champagne is really made in the region of France that originated this kind of wine.
There are many excellent olive oils that are not designated 'D.O'. This is because they draw their olives from diverse areas, rather than being grown in one region.