When you come to metaphorical "fork in the road" you generally have two options to take, and your decision effects your future. Computer programs reach this fork in the road when they hit the fork() system call.
At this point, the operating system will create a new process that is exactly the same as the parent process. This means all the state that was talked about previously is copied, including open files, register state and all memory allocations, which includes the program code.
The return value from the system call is the only way the process can determine if it was the existing process or a new one. The return value to the parent process will be the Process ID (PID) of the child, whilst the child will get a return value of 0.
At this point, we say the process has forked and we have the parent-child relationship as described above.