This is a hair net for your thread.  It prevents the thread from behaving badly as it comes off the reel.  This is vital for metallic threads and for rayon thread on the high speed domestic machines.   The net can be cut in half and used for two 5000m spools.   If cut into three pieces, it can be used for three 1000m reels.
The nets can also be used to keep the thread from untangling during storage.