Thy love hath made the world forget the loves of long ago.
When once thy name was on the tongue, the lovers caught it
And it set the speakers and the hearers dancing to and fro
(Sa'di, Muslihu'd-Din of Shiraz)
In general. I'm going to take this advice so if you want a well-researched, accurate account pf the story of Layli do your own googling. Just briefly, possibly inaccurately, and mostly from Wikipedia it seems:
The story originated in the seventh century in a real event where a young man (Qays) and young woman (Layli or often Layla) fell in love but were prevented from marrying by family pressure. The knowledge that Layli had been married to another drove Qays insane hence he became known as 'Majnun' which means, quite simply, 'mad'. He spent the rest of his life wandering disconsolately on the fringes of society, supposedly continually searching for Layli.
The story has been picked up and reworked by many great Middle Eastern writers and has even been claimed as the source for Romeo and Juliet though scholarly opinion is against that idea.
In the hands of those influenced by Sufi thought the story takes a religious turn with Layli signifying 'the Beloved' - the Divine Essence - and Majnun standing for Everyman constantly, obsessively seeking the presence of the unknowable God.
The story of Majnun and Layli makes only a couple of brief but powerful appearances in the Baha'i Writings where Baha'u'llah speaks with approval of the intensity of Majnun's search.
Yea, although to the wise it be shameful to seek the Lord of Lords in the dust, yet this betokeneth intense ardor in searching. "Whoso seeketh out a thing with zeal shall find it."
For Baha'is, of course, being mentioned by Baha'u'llah, is the highest pinnacle the story could have reached but others may be further impressed by the fact that the guitar god himself, at the time manifesting himself as Derek and the Dominos, named a song and indeed an album after Layla.
It is important to remember that for speakers of the original languages the hero of all versions of this tale is known as 'the insane'. It is as though 'Romeo and Juliet' was actually called 'Juliet and the Loony'.
Religions, including the Baha'i Faith, by and large are (and certainly like to be thought of as) practical, sensible, organisations working to make this world a better place. Perhaps, Baha'u'llah's endorsement of Majnun may help to remind us that religion can also be an obsessive search for the Unknowable, Unfindable which can make us appear and even be quite crazy.
When once the seeker hath ascended unto this station, he will enter the City of Love and Rapture, whereupon the winds of love will blow and the breezes of the spirit will waft. In this station the seeker is so overcome by the ecstasies of yearning and the fragrances of longing that he discerneth not his left from his right, nor doth he distinguish land from sea or desert from mountain.
Love accepteth no existence and wisheth no life: He seeth life in death, and in shame seeketh glory. To merit the madness of love, man must abound in sanity; to merit the bonds of the Friend, he must be full of spirit.