Octane is gasoline's resistance to preignition as rated on a scale. The higher the octane number the less likelyhood of preignition (spark knock).
Two methods of measuring octane are available: Research and Motor. The numbers do not correspond between them, but are close. The number on the fuel pump, 82/87/92/101 is an average of the two.
Generally, you should use the lowest octane number that allows you to operate your engine without knocking in the way you use it.
Jim