According to Ireland's Eye:
The bean-sidhe (woman of the fairy) may be an ancestral spirit appointed to forewarn members of certain ancient Irish families of their time of death. According to tradition, the banshee can only cry for five major Irish families: the O'Neills, the O'Briens, the O'Connors, the O'Gradys and the Kavanaughs. Intermarriage has since extended this select list.Here is a more detailed description from Irish Culture and Customs:
The Bean Sidhe or Banshee makes her appearance when someone in the household is about to die. She haunts only the families of the "high Milesian race" - those whose names have an "O", "Mac" or other prefix. One exception to this rule has been granted by virtue of the Irish poets who have given her to some of the Norman-Irish families - the FitzGerald's for example. In any event, she heralds the demise of only those who are of authentic noble stock and it is with great dread when her piercing "caoine" or keening is heard. In many respects, this mysterious creature resembles traditional Irish keeners or mourners of old; as with her mortal counterparts, those who have seen her describe her as drawing a comb through her hair, similar to tearing the hair out in anguish, which the ancient mourners used to do. Incidentally, or maybe not, while the Banshee is considered benign, she supposedly has a sister force who isn't; this force is called the Lianhan Sidhe and her sole purpose is to seek the love of mortal men. Their desire for her ultimately destroys them.The banshee, according to legend, is usually heard at night, but sometimes in the morning, and at noon. An old Irish poem refers to the appearance of the Banshee in the morning:
Hast thou heard the Banshee at morn,There were a few banshee stories among some of my older relatives. (I suppose being descended from the Kavanaughs and the O'Neills as well as the O'Connors made them especially worthy of hauntings!) Irish lore is full of tales of the preternatural; the banshee is definitely one of the most interesting.
Passing by the silent lake,
Or walking the fields by the orchard?
Alas! that I do not rather behold
White garlands in the hall of my fathers.