Firstly, pnellesen is incorrect; you can use single or double quotes in $_POST[] vars, just like any other array.
xhi is correct, in that you must use double-quotes around your string if you wish to include variable names in it to be translated.
However, that isn't the whole story. If you are embedding an array variable into a string like this, you must wrap it in curly braces, otherwise the PHP interpreter gets confused by the array variable syntax.
So your code would need to look like this:
PHP Code:
$query = "SELECT * FROM table WHERE field='{$_POST[department]}'";
One other thing I would add: Please also be very careful when putting a post variable directly into a SQL query -- you may be opening yourself up to a potential security problem, called an "SQL injection attack", where malicious posters could manipulate your SQL string and hack your database.
Hope you get everything working
All the best.