Postfix mail server run script

First, go to master.cf and register your script "myhook" by adding the following line:

myhook unix - n n - - pipe flags=F user=www-data argv=/path/to/script.sh ${sender} ${size} ${recipient}

Also, edit smtp line to tell Postfix to run the filter for any mail arriving via the SMTP delivery:

smtp      inet  n       -       -       -       -       smtpd        -o content_filter=myhook:dummy

Please note that if you are sending mails using the "sendmail" command, the filter will not trigger. In this case, add the option after the "pickup" delivery method:

pickup    fifo  n       -       -       60      1       pickup -o content_filter=myhook:dummy

Restart postfix: postfix reload

Make your script readable and executable by anybody: chmod +rx script.sh

Note that script is always triggered for any mail arriving. To specify exact address see @MariusMatutiae answer.