Antioxidants are compounds that slow down oxidation. In olive oil they are mainly polyphenols and vitamin E. They capture reactive oxygen compounds before these can attack the fatty acids.
For the oil itself this means it stays fresh for longer and copes well with heat. That is why a good extra virgin olive oil is more stable in the pan than many people think. How many antioxidants an oil brings depends on the variety, the time of harvest and fast processing.