In multitasking operating systems, a child process is a process that has been started by some other process (commonly know as parent process). The processes form a tree (process tree).
In UNIX, the only process that doesn't have a parent process is PID 1, usually init, the process that starts all daemons at boot, shuts them down at shutdown, and manages gettys in between those things. Any process can create child processed by using fork() system call (that effectively splits the process in two halves, parent and child).
Also, in BatMUD, there are child processes under the Bat City clock tower. They are small creatures that look at you with their sad green eyes and ask for road to home. Only heartless killers can kill them.
(I did that once, later realized my utter cruelty, and now I hate myself for allowing that to happen.)