-o comm= means user output should be the command name only, but without any column title. E.g. if you do -o comm=COMMAND, it will print you a column title COMMAND:
$ ps -o comm= -p $PPID
xterm
$ ps -o comm=COMMAND -p $PPID
COMMAND
xterm
-p $PPID selects the process by the given parent's PID, the PPID.
That means -o comm= -p $PPID are two independent options.
So your command essentially does give you the name of the parent process by its PPID.
E.g. if I start tmux, it has the PID of 1632. Now I start several bash in each pane, which each have the PPID of 1632, but have their own PID.
You can learn more in What are PID and PPID?
I am not sure, but ps might look at /proc/$PPID/comm to determine the parent's command name.
In my case, executing this command gives you the name of the parent's process, without using ps:
$ cat /proc/$PPID/comm
tmux
$ cat /proc/1632/comm
tmux
psjust has a switch case that prints out given columns, if the-ooption is given, and a header for each column that has a string following the=. – polym Jul 21 '14 at 21:02