Heres a description from the extension I would look to implement:
Can you indicate via the poll (or comment below) if you would find this feature useful?phpBB does not provide the ability to send regular emails to users with summarized postings on a board. Instead, phpBB expects that users will visit the phpBB board regularly if they want to keep up with what is going on at the site.
phpBB Digests are emails sent to users periodically with summary of postings made on the board for discrete time periods. Digests makes some phpBB board users’ lives easier. They don’t have to explicitly visit the site to see what conversations are going on around there. They just read their digest and if there is some topic that seems of interest, they click on the topic link in their email program and start participating! They can unsubscribe at any time. By default, weekly digests are sent on Sundays. The users determines the hour they want to receive the digest. Whatever time they choose, they will always get the latest news so they can pick a time that suits their lifestyle.
Digests can be daily, weekly or monthly. Posts older than this will not be sent in a digest. In addition, if you want you can elect not to see posts since you last logged in, if you visited recently. You can even filter out your own posts.