The file /dev/ptmx is a character file with major number 5 and minor number 2, usually of mode 0666 and owner.group of root.root. It is used to create a pseudoterminal master and slave pair.
When a process opens /dev/ptmx, it gets a file descriptor for a pseudoterminal master (PTM), and a pseudoterminal slave (PTS) device is created in the /dev/pts directory. Each file descriptor obtained by opening /dev/ptmx is an independent PTM with its own associated PTS, whose path can be found by passing the file descriptor to ptsname(3).
Before opening the pseudoterminal slave, you must pass the master's file descriptor to grantpt(3) and unlockpt(3).
Once both the pseudoterminal master and slave are open, the slave provides processes with an interface that is identical to that of a real terminal.
Data written to the slave is presented on the master file descriptor as input. Data written to the master is presented to the slave as input.
In practice, pseudoterminals are used for implementing terminal emulators such as xterm(1), in which data read from the pseudoterminal master is interpreted by the application in the same way a real terminal would interpret the data, and for implementing remote-login programs such as sshd(8), in which data read from the pseudoterminal master is sent across the network to a client program that is connected to a terminal or terminal emulator.
Pseudoterminals can also be used to send input to programs that normally refuse to read input from pipes (such as su(1), and passwd(1)).
The Linux support for the above (known as UNIX 98 pseudoterminal naming) is done using the devpts filesystem, that should be mounted on /dev/pts.
Before this UNIX 98 scheme, master pseudoterminals were called /dev/ptyp0, ... and slave pseudoterminals /dev/ttyp0, ... and one needed lots of preallocated device nodes.