What does ^ character mean in grep ^d?

The caret ^ and the dollar sign $ are meta-characters that respectively match the empty string at the beginning and end of a line.The grep is matching only lines that start with "d".

To complement the good answer by The New Idiot, I want to point out that this:

ls -l | grep ^d

Shows all directories in the current directory. That's because the ls -l adds a d in the beginning of the directories info.

The format of ls -l is like:

-rwxr-xr-x  1 user group    0 Jun 12 12:25 exec_file
-rw-rw-r--  1 user group    0 Jun 12 12:25 normal_file
drwxr-xr-x 16 user group 4096 May 24 12:46 dir
^
|___ see the "d"

To make it more clear, you can ls -lF to include a / to the end of the directories info:

-rwxr-xr-x  1 user group    0 Jun 12 12:25 exec_file*
-rw-rw-r--  1 user group    0 Jun 12 12:25 normal_file
drwxr-xr-x 16 user group 4096 May 24 12:46 dir/

So ls -lF | grep /$ will do the same as ls -l | grep ^d.

It has two meanings. One as 'The New Idiot' above pointed out. The other, equally useful, is within character class expression, where it means negation: grep -E '[^[:digit:]]' accepts any character except a digit. The^` must be the first character within [].