TTY stands for Text Telephone, which is sometimes called a Telecommunication Device for the Deaf (TDD). TTY, however, is the the more commonly used term.
A TTY is a typing device which lets people who are deaf, hard of hearing, or speech-impaired use the telephone to communicate. With a TTY messages can be typed back and forth in place of talking and listening. Note that a TTY is needed to communicate another TTY, however a Telecommunications Relay Service (TRS) can be dialed in order to contact someone using a TTY.
711 is the universal number to dial within the United States to connect to a TRS operator. Both voice and TTY calls can be made to 711 for free. With a voice call, a TRS operator will type what you say so that the person you are calling can read the words on their TTY display. When they respond, the TRS operator will read aloud what was sent for you to hear over the phone.
More Information on 711 is available from the Federal Communications division.