This might be usefull if you would like to force people coming back to the forums to read their Private Messages instead of having all the information already send by email.

AdminCP -> Languages & Phrases -> Search in Phrases

Search for pmreceived in Phrase Variable Name Only.

Click Edit for the phrase Email Body Text Phrases Containing 'pmreceived'

You can use for example

Dear $touserinfo[username],
You have received a new private message at $vboptions[bbtitle] from $fromusername, entitled "$plaintext_title".
To read, respond to, or delete the message, you must log in here:
All the best,
and paste it into English (US) Translation (Optional) and save it.

People are now forced to return to your forum to check the private messages they have received.