Why do cat5 cables sometimes have the fluffy fiber bit in them?
Actually it's for pulling the outer shielding away from the inner wires. When you're punching down the cable you pull the fiber string down from the top of the cable and it makes a nice split in the outer shielding that allows you to pull the outer shielding down to cut it off without damaging the inner wires. Here's a video that shows the process:
In addition to Joe's answer; It adds some strength to the cable for pulling and helps prevent damage to the copper wires. For example, when you are pulling long runs.