Olive oil is one of the few good vegetable oils. It is about 10% omega-6 (n-6) fatty acids, compared to 50% for soybean oil, 52% for cottonseed oil and 54% for corn oil. Omega-6 fatty acids made up a smaller proportion of calories before modern times, due to their scarcity in animal fats. Beef suet is 2% n-6, butter is 3% and lard is 10%. Many people believe that excess n-6 fat is a contributing factor to chronic disease, due to its effect on inflammatory prostaglandins. I'm reserving my opinion on n-6 fats until I see more data, but I do think it's worth noting the association of increased vegetable oil consumption with declining health in the US.
Olive oil is also one of the few oils that require no harsh processing to extract. As a matter of fact, all you have to do is squeeze the olives and collect the oil. Other oils that can be extracted with minimal processing are red palm oil (9% n-6), hazelnut oil (10% n-6) and coconut oil (2% n-6). These are also the oils I consider to be healthy. Due to the mild processing these oils undergo, they retain their natural vitamin and antioxidant content.
You've eaten corn, so you know it's not an oily seed. Same with soybeans. So how to they get the oil out of them? They use a combination of heat and petroleum solvents. Then, they chemically bleach and deodorize the oil, and sometimes partially hydrogenate it to make it more shelf-stable. Hungry yet? This is true of all the common colorless oils, and anything labeled "vegetable oil".
Olive oil is great, but don't run out and buy it just yet! There are different grades, and it's important to know the difference between them. The highest grade is extra-virgin olive oil, and it's the only one I recommend. It's the only grade that's not heated or chemically refined in any way. Virgin olive oil, "light" olive oil (refers to the flavor, not calories), "pure" olive oil, or simply olive oil all involve different degrees of chemical extraction and/or processing. This applies primarily to Europe. Unfortunately, the US is not part of the International Olive Oil Council (IOOC), which regulates oil quality and labeling.
The olive oil market is plagued by corruption. Much of the oil exported from Italy is cut with cheaper oils such as colza. Most "Italian olive oil" is actually produced in North Africa and bottled in Italy, and may be of inferior quality. The USDA has refused to regulate the market so they get away with it. If you find a deal on olive oil that looks too good to be true, it probably is.
Only buy from reputable sources. Look for the IOOC seal, which guarantees purity, provenance and freshness. IOOC olive oil must contain less than 0.8% acidity. Acidity refers to the percentage of free fatty acids (as opposed to those bound in triglycerides), a measure of damage to the oil. Fortunately, the US has a private equivalent to the IOOC, the California Olive Oil Council (COOC). The COOC seal ensures provenance, purity and freshness just like the IOOC seal. It has outdone the IOOC in requiring less than 0.5% acidity. COOC-certified oils are more expensive, but you know exactly what you're getting.
Thanks to funadium for the CC photo