Ben,

Index creates an array of values, in this case True/False for each comparison of cells A1:A3 to B2. So if A2 actually is equal to B2, then it would create an array of {FALSE,TRUE,FALSE}
The OR function looks for any instances of TRUE and if it finds any, then the OR function returns TRUE, so in this example it would return TRUE because A2=B2. Only if there are no TRUE values at all will the OR function return FALSE.

That all being said, there is no reason to use OR(INDEX over COUNTIF for this task.