$# Stores the number of command-line arguments that
were passed to the shell program.
$? Stores the exit value of the last command that was
executed.
$0 Stores the first word of the entered command (the
name of the shell program).
$ Stores all the arguments that were entered on the
command line ($1 $2 ...).
"$@" Stores all the arguments that were entered
on the command line, individually quoted ("$1" "$2" ...).
So basically, $# is a number of arguments given when your script was executed. $ is a string containing all arguments. For example, $1 is the first argument and so on. This is useful, if you want to access a specific argument in your script.

As Brian commented, here is a simple example. If you run following command:

./command -yes -no /home/username
$# = 3
$* = -yes -no /home/username
$@ = array: {"-yes", "-no", "/home/username"}
$0 = ./command, $1 = -yes etc.