TCPMAN is a utility for manual or script modem dialing that is used when accessing the Internet. TCPMAN comes with the shareware program, Trumpet Winsock. Winsock is an interface between an application program in a Windows operating system and the Internet's Transmission Control Protocol program. (There are other Winsock programs than Trumpet's, which was one of the first and is among the most widely installed today.)
TCPMAN is the "tcpman.exe" file in Trumpet Winsock. Although the "MAN" stands for "manual," most users set up or are provided with a script of modem AT commands that is processed automatically each time you start TCPMAN. This is viewed as "scripted manual dialing." Using the information about your modem that you provide during setup, TCPMAN negotiates the actual line speed and other characteristics of the connection between your modem and the modem that is being dialed.
Typically, you will know about TCPMAN if you are with a service provider that furnishes or requires you to have the Trumpet Winsock. If not, your dialing capability is furnished by some other program.