This would be true for repeated characters, since indexOf finds the first index of a string, and you're searching from the end. Example:
var a = "xyzxyz";
On first iteration, i === 4, a.charAt(4) === "x", and a.indexOf("x") === 0. So 4 !== 0.
It then sets a = a.substring(0, 4) + a.substring(5). Recalling at substring is inclusive in the first index but exclusive in the last index, that means in this case a = "xyz" + "yz", so we have removed the duplicate "x" from the string.
Since the loop traverses backward, this will continue to work even for characters repeated more than once; you can see that the portion a.substring(i + 1) will always have been covered by the algorithm already, i.e. not contain any duplicates.
As always when encountering this type of thing, applying the extract method refactoring would be a great way to make the code clearer. (Even better than commenting it!) So if you just pulled this out into a method, the code could become a = removeDuplicateChars(a), and everyone is much happier.