A process group is a unix kernel concept. It doesn't come up very often. You can send a signal to all the processes in a group, by calling the
kill system call or utility with a negative argument.
When a process is created (with
fork), it remains in the same process group as its parent. A process can move into another group by calling
setpgrp. This is normally performed by the shell when it starts an external process, before it executes
execve to load the external program.
The main use for process groups is that when you press
Ctrl+\ to kill or suspend programs in a terminal, the terminal sends a signal to a whole process group, the foreground process group. The details are fairly complex and mostly of interest to shell or kernel implementers; the General Terminal Interface chapter of the POSIX standard is a good presentation (you do need some unix programming background).
Jobs are an internal concept to the shell. In the simple cases, each job in a shell corresponds to a process group in the kernel.