In just about every ratchet set I’ve seen, there is included a thin, saw-toothed, plastic disc made to mate with the handle, in the same manner a socket would, but it is paper-thin. What is this thing, and what purpose can it possibly serve???
Thanks,
You clip it between the socket and the ratchet. It can be a lifesaver when you have to start a bolt in a tight space. It lets you spin the socket while using the ratchet to hold the bolt steady. A Snap-On dealer gave me a nice 3 piece set about 20 years ago, I haven’t used them much but I was glad I had them when I did neet them. I used one a few weeks ago to get the back spark plugs started in my wife’s Ford Taurus.
Not useless. It’s good to have and bad when you need it but don’t have it. 
I had a drawer in my rollaway for useless tools that I bought (stuff I thought would work but didn’t live up to its hype). There were about 3 tools in there, tops.
Note as well that many types of ratchets come with a toothed metal disk integral to the ratchet. My “lady slimline” stainless Craftsman ones have this.
To add to what Racer said, it’s useful for starting a bolt in a tight space. Especially when the bold is still lose enough that the racheting(sp?) action doesn’t work. You use that with your thumb and forefinger to get the bolt tight enough that the ratchet actually works.