It's an attachment that would go where a stock would go on a large format pistol (AR pistol, AK pistol, etc) that allows disabled people to use these weapons single handedly (especially if they only have 1 hand) more easily.
There is usually a strap or some other way to attach them to the forearm. This provides more support and another point of contact.
ATF approved them around 2012.
Shortly thereafter non disabled people realized that you could put the rear of the brace against your shoulder in the same way you would a stock. It became a work around for SBRs and SBSs.
ATF shit themselves.
Since then ATF has gone back and forth about whether or not you could shoulder a brace, and if so, how often. But they were always legal.
Now they have released a rule mostly making them illegal (except under the light of a full moon on the 5th Tuesday of Months that end in z if you sacrifice a child to be sniffed by Biden).
As the legal eagles dig deeper into the rule more and more shenanigans come to light.
For example you can register your (now) SBR as an NFA item for free for 120 days after the rule was posted. Except that they can't get all the potential registrations done within the time limit so your registration will time out and automatically be denied. And by attempting to register you are sending ATF proof of your possession of an illegal (suddenly) SBR. Along with your address, fingerprints, photograph, etc.
And if your (just turned into an) SBR is an import then the brace was part of it's 922r compliance so simply removing the brace and destroying the brace or giving it to the popo will not suffice. You have to hand in your entire (Surprise! You've got an) SBR to the cops.
And if you do turn it in, get a receipt. In fact I would recommend video recording the whole process. If ATF comes knocking I doubt the Hunter Biden defense, "My wife threw it in the trash", will satisfy them.
The industry estimates between 10 million and 40 million braces are in circulation. Meaning millions of people who were legal can suddenly become felons without actually doing anything wrong.