What is the meaning of "ps -aef | grep $(pwd)" command?

From the man page for ps:

   -a              Select all processes except both session leaders (see getsid(2)) and
                   processes not associated with a terminal.

   -f              Do full-format listing. This option can be combined
                   with many other UNIX-style options to add additional
                   columns. It also causes the command arguments to be
                   printed. When used with -L, the NLWP (number of
                   threads) and LWP (thread ID) columns will be added. See
                   the c option, the format keyword args, and the format
                   keyword comm.
   -e              Select all processes. Identical to -A.

grep is used to print lines matching a pattern.

What it does

The command

ps -aef | grep `pwd`

prints out all the lines matching the output of the command pwd(which will be the path your current working directory), from the output of ps -aef.

e.g:

saji@geeklap:~$ pwd
/home/saji

saji@geeklap:~$ ps -aef | grep `pwd`
saji      2854  2814  0 09:51 ?        00:00:00 /usr/bin/ssh-agent /usr/bin/gpg-agent --daemon --sh --write-env-file=/home/saji/.gnupg/gpg-agent-info-geeklap /usr/bin/dbus-launch --exit-with-session gnome-session --session=ubuntu
saji      2855  2814  0 09:51 ?        00:00:00 /usr/bin/gpg-agent --daemon --sh --write-env-file=/home/saji/.gnupg/gpg-agent-info-geeklap /usr/bin/dbus-launch --exit-with-session gnome-session --session=ubuntu
saji      2879     1  0 09:51 ?        00:00:00 /usr/lib/gvfs//gvfs-fuse-daemon -f /home/saji/.gvfs
saji     14242 14148  0 15:26 pts/7    00:00:00 grep --color=auto /home/saji

As you can see the output shows the lines matching my current working directory, which is /home/saji.

Background info:
If a command is in $(...) or ..., then the command is run and the output (what is printed to the screen) is caught and substituted to where the original $() or `` string was. So the actual command run is grep pwd.

For more information refer this link.(Thanks to @minerz029 for this information).

Do check out the following link for a detailed technical answer from the man pages itself:

http://explainshell.com/explain?cmd=ps+-aef+|+grep+%60pwd%60

ps -aef | grep $(pwd)

Searching,Getting and displaying full information about the list of processes which are associated with the working directory and print the path of that directory.