To understand olive oil, you must understand how the oil was obtained from the olive and if it has undergone a mechanical or a chemical process to achieve its flavor, color and acidity.
Virgin olive oil is made with no chemical treatment using solely physical means to extra oil from the olive fruit. Extra virgin olive oil is the highest quality of olive oil, because it has the lowest acidity of any olive oil. Extra virgin olive oils vary widely in taste, color and appearance. Note that "extra virgin" may be used without legal restrictions.
Refined olive oil has been chemically treated for taste and acidity, but loses some of its nutritional properties. It has a high acidity level, making it a lower grade olive oil.
An olive oil can be a blend of both virgin and refined olive oils. It is made by taking lower quality refined olive oil and adding virgin olive oil to create a medium grade olive oil. The term olive oil refers to this blend. Thus, “100% Pure Olive Oil" is often the lowest quality available: higher grades would have "virgin" on the label. The term "Pure" does not refer to anything in the production of olive oil and is a widely used but unregulated marketing term.
Also, in the US the term "cold-pressed" is largely unregulated, as is "first press." The terms refer to how olive oil was made many decades ago, and do not apply to how the vast majority of oil is made today. There is no second pressing, and the technology used today to make olive oil does not use hot water or high temperature steam that used to degrade flavor during production.
Because olives are a fruit, olive oil is considered a fruit juice and should be treated as such when storing olive oil. Air, heat and light can cause olive oil to turn rancid, or oxidize. It should be stored in a cool-to-room-temperature, dark location in an airtight container. Olive oil does not need to be refrigerated.
How to find a great olive oil? Look for a virgin or extra virgin olive oils, and have fun tasting!