What is a TTY adaptor used for?

It is a device for the deaf to communicate via phone. Basically 'texting' each other on a specific machine about the size of a laptop these days. Maybe the adapter allows you to call/type with a deaf person who have a tty or tdd machine. I have one at my home since am deaf. The technology is amazing now that most of my deaf friends and I communicate via pager/ hearing through relay service through our pagers or computer.

http://en.wikipedia.org/wiki/TTY

yep that's it. Good answer.

The answer is probably not correct.
While in the old days tty stood for teletype, the term tty device now includes aids or devices that allow partially deaf people to hear by increasing the volume or by some other modification of the sound. However, these devices expect a particular ‘pin-out’, or the assignment of the pins or rings on the connector. Device manufacturers, like Nokia or Apple, make lots of money by selling accessories and they want to force people to by their branded accessories. So, they choose a non-standard pin-out, -thus preventing standard head-sets from being usable. However, since we are sort of a civilized country, we do require them to allow connection of tty devices! So they quietly sell ‘tty adapters’ which basically convert the non-standard pinout to standard pinout. This way they satisfy the law. But most apple customers unlikely to tech-savvy, so they don’t know all these little tricks and end up buying Apple or Nokia headsets making Steve Jobs a very happy man : )

So, yes, it is a headset adapter you bought. It will let you use a standard headset (say Plantronics) with your apple iphone (or whatever shiny thing you bought from apple).