The birthday of Our Lady and the calendar
The Church celebrates only three earthly birthdays: those of Our Lord, St John the Baptist and Our Lady. The Golden Legend relates that for a long time the date of the birth of Our Lady was not known:
"And the day of the nativity was not known in long time of good christian men, and as master John Beleth saith that, it happed that a man of good contemplation every year in the sixth ides of September was in prayer, and he heard a company of angels that made great solemnity. And then he required devoutly that he might have knowledge wherefore every year only on that day he heard such solemnity and not on other days.
And then he had a divine answer that, on that day the blessed Virgin Mary was born into this world, and that he should do it to be known to the men of holy church, so that they should be concordable to the heavenly court in hallowing this solemnity."
It also adds a nice story about the establishment of the (now defunct) octave for the feast:
"And when he had told this to the sovereign bishop the pope, and to the others, and had been in fastings, in prayers, and sought in scriptures and witnesses of old writings, they established this day of the nativity of the glorious Virgin to be hallowed generally of all christian men, but the octaves sometime was not hallowed ne kept. But Innocent the fourth, of the nation of Genoa, ordained and instituted the said octave to be observed. And the cause was this:
After the death of Pope Gregory, anon the citizens of Rome enclosed all the cardinals in the conclave because they should purvey lightly for the church, but they might not accord in many days, but suffered of the Romans much sorrow. Then avowed they to the Queen of Heaven that if they might go quiet from thence they should establish to hallow the octaves of the nativity which they had long negligently left. And they then by one accord chose Celestin, and were delivered, and accomplished then their avow by Innocent, for Celestin lived but a little time, and therefore it might not be accomplished by him."
The Little Office of Our Lady
The Little Office came into use around the eight century is believed to have been made compulsory for clerics by Urban II, in aid of the Crusades. Monasteries generally said it each day in addition to their standard Office (today only the Carthusians maintain this practice as far as I know), and it was extremely popular amongst the laity, many of whom learnt to read using Books of Hours.
The Little Office largely fell out of use during the Counter-Reformation (aside from some women's monasteries who used it instead of the full Office), not least because Pius V made it optional for clerics and monasteries (and as we all know, optional generally means it doesn't get done at all!) as part of his liturgical clean-up job.
Baronius Press, however, has recently put out a rather nice new edition including all of the relevant chants of the Little Office. But while you wait for your copy to arrive there are some excellent resources on the net that you can use. First you can find a full set of all of the Hours ready to download here. Secondly, and most usefully of all, Sentire Cum Ecclesia has pointed to a great site well worth exploring with audiofiles (said not sung alas!) of Prime and Compline of the Little Office.