The term Breton Lay (or Lai) are most famously related to the works of Marie de France, but appear to be of much older origin. The word lai probably comes from the Gaelic word laid. It is speculated that the word Breton here means Celtic in general, rather than specifically of Brittany.
In a 12th Century context, a lai is a short frech poem, in the general format of a love story, often with some element of trajedy. The lai is a typical venue for early stories of courtly love, but retain elements of the suprenatural and faery from the celtic stories many are drawn from.
From the 13th century the word lai seems to have shifted meaning, and instead applied to a long narrative poem.
Ample literary evidence points to lays traditionally being accompanied by music, for instance the following excerpt from Lay of Graelant (trans. Weingartner)
L'aventure de Graelent
Vos dirai si com je l'entent;
Et les notes a retenir.
The adventure of Graelent
I will tell you as I understand it;
The Lay is good to hear
And the melody good to remember.