Abbreviation for TeletypeWriter eXchange, a teletype service begun by AT&T in 1931 and sold to Western Union in the early 1970s. It used machines with three-row keyboards operating at 60 words per minute. Connections were originally routed through a manually-switched network separate from the regular telephone network. In mid-1962, AT&T began integrating TWX service with the "direct distance dialing" (long-distance) network along with WADS (see for more information).
Reference:
Cuccia, Mark J. "HISTORY/twx.1961.automation.plans." 16 Jan. 1997.
Townson, Patrick A. "TWX 1961 Automation Plans." 23 Jan. 1997. TELECOM Digest & Archives. http://hyperarchive.lcs.mit.edu/telecom-archives/archives/history/twx.1961.automation (4 Jun. 2001).