I would like to modify the content of the email received by users who are in receipt of a private message on the boards.

How do I make the changes?

Humm?? That is a very broad question.
It would be in the language files but are you talking subject,body header footer?
Or are you looking to chage the appearance of the email which is in the style editor.

Anyway quick down and dirty you would start in:
Control Panel » Languages » Language Editor
select mailer.php for the language file.
Scroll down the list and find PMN_SUBJECT for a key field.
That should be your starting point.
Bear in mind that the emails are sent as text and html so you will see some redundant fields that need to be edited since there is one for most each sent method.
Is is easier if you can print a email sent and then look for what you want to change.