Ignoring its intended meaning, this is most likely where you’ll see it used:
>>> 0 is unique in that it is the only operator that will convert any type to a positive integer:
"string" >>> 0 == 0
(function() { }) >>> 0 == 0
[1, 2, 3] >>> 0 == 0
Math.PI >>> 0 == 3
In your example, var len = this.length >>> 0, this is a way of getting an integer length to use to iterate over this, whatever type this.length may be.
Similarly, ~~x can be used to convert any variable into a signed integer.