The "controlling terminal" is an attribute of a process that identifies the terminal device that affects it with regards to "job control". It typically affects processes that run inside a terminal or open a terminal device.
Controlling terminal is a terminal that is attached to a process to send it signals like Ctrl-C from user.
A process can be run without a controlling terminal, see Process without a controlling terminal. Processes without controlling terminal are marked with ?? in the ps output.
https://en.wikipedia.org/wiki/POSIX_terminal_interface#Controlling_terminals_and_process_groups
