The monks are, of course, already making available audio recordings of their daily Mass and this addition now makes Sung Vespers, in a Benedictine form of the Divine Office, available to a wider public, thus facilitating greater access to sung Sunday and Festal Vespers than has heretofore been available to the general Catholic public -- not, mind you, as it might be sung by a professional choir of course, but rather Vespers sung from within the intimacy of the monastic community and as part of the day-to-day exercise of the monastic horarium.
It is certainly my own hope that, in addition to providing people with the opportunity to listen in each week, on feast days, or with whatever frequency they may choose, this might further inspire people to take up the praying of the Divine Office as part of their own personal spiritual practice, and also encourage priests and parishes to make sung Sunday Vespers available as part of their own parish liturgical life -- both of which were encouraged by the Second Vatican Council.
Some Practical notes
Vespers will be recorded and made available on their proper day, thus providing the opportunity to listen to the Office on its proper day. This will be particularly the case for North American time zones. Western European listeners are likely to see the recordings available sometime in the latter part of the evening.
The NLM is providing a graphical link in the left sidebar which will take you to these recordings, while also providing a easy reminder of their availability, if not also a general reminder about the Divine Office.
Other Catholic websites and blogs are more than welcome to place a copy of this graphic on their own sites in order that the Divine Office and Sunday Vespers might be promoted. (I would only ask that you upload this graphic to your own sites, rather than linking to the graphic here, which can cause bandwidth issues.) I would personally recommend you make this graphic linkable and link it to this page: "http://osbnorcia.org/?page_id=843. If help is needed in setting this up, please don't hesitate to contact me.
Finally, I would make note that the monks are doing this based on the limited resources they have. If anyone is so inclined, I am sure they would benefit greatly from donations toward audio recording and publishing resources, or even those that might allow them to broadcast live. Do give it some consideration.