Whilst the operating system can run many processes at the same time, in fact it only ever directly starts one process called the init (short for initial) process. This isn't a particularly special process except that its PID is always 0 and it will always be running.
All other processes can be considered children of this initial process. Processes have a family tree just like any other; each process has a parent and can have many siblings, which are processes created by the same parent.
Certainly children can create more children and so on and so forth.
1 init-+-apmd |-atd |-cron ... 5 |-dhclient |-firefox-bin-+-firefox-bin---2*[firefox-bin] | |-java_vm---java_vm---13*[java_vm] | `-swf_play
 The term spawn is often used when talking about parent processes creating children; as in "the process spawned a child".