A TTY is a device like a typewriter that has a small readout. It is also called a Telecommunication Device for the Deaf (TDD) but that name has been devised by the hearing community and is not accepted by Deaf people, the actual users of TTY technology. They still prefer the term, TTY.
A TTY can be used to send text over the phone. Someone who cannot hear can then use the phone by typing what they want to say and reading what the other party says.
A person using a TTY can converse directly over the phone line with anyone else who is using a TTY (and in some cases with someone who have a computer). A person using a TTY can even converse with someone not using a TTY via relay.
Most TTYs use Baudot and can only connect directly to another TTY or to any phone via relay. Some TTYs can also use ascii, so they can also connect to a computer.
The original TTY was developed by a Deaf man, and it was a sort of confirmation of the saying that "necessity is the Mother of invention".
Simple TTYs just have rubber cups into which the earpiece and speaker of a phone handset can be placed. Since they communicate simply using sounds that represent characters, they can use any phone, except cellphones. Cellphones use various digital and analog technologies to send their signals, so the tone equals character technique is disrupted.
Some newer cellphones do support some newer TTYs.
Extra features on some TTYs include printers, memories, and some are now pocket-sized and battery operated.
There are also incoming only (VCO) devices that use can display text of an incoming TTY call, see the Speak and Read
For the latest information on TTYs, see this Google Search.