What is the meaning of [Rhyme nor reason]

A thing which has neither rhyme nor reason makes no sense, from either a poetic or logical standpoint.

‘Rhyme or reason’ is first recorded by John Russell, in The Boke of Nurture, circa 1460:

As for ryme or reson, ye forewryter was not to blame,
For as he founde hit afore hym, so wrote he ye same.