What's the meaning of the phrase 'Moot point'?
An irrelevant argument.
What's the origin of the phrase 'Moot point'?
Some may disagree with the above meaning and argue that it means 'a point open to debate', rather than 'a point not worth debating'. That former meaning was certainly the correct one when the term was first coined, but that's going back a while.
Laurence Humphrey, the president of Magdalen College, Oxford, wrote Nobles or of Nobilitye, a manual of behaviour for the English nobility, in 1563. In that he wrote:
"That they be not forced to sue the lawe, wrapped with so infinite crickes and moot poyntes."
In medieval England, moots, or meets, were assemblies or councils where points of government were debated. The country was split into juridicial areas called hundreds and administered via assemblies known as hundredmotes. The form of government has long since vanished but the term hundred is still in use as the name of the procedural device which gives consent to MPs' resignation. British MPs aren't allowed to resign and, when members wish to leave Parliament they may do so by applying for the notional position of Crown Steward and Bailiff of the Chiltern Hundreds. In such assemblies points which were put up for discussion were said to be mooted.
The change in meaning has come about following the introduction of 'moot courts', which are session where law students train for their profession by arguing hypothetical cases, that is, 'moot points'. The lack of any substantive outcome from these theoretical cases has led to the 'unimportant/not worth discussing' meaning of 'moot point', which is what many people accept today.
A further step, and one which it is to be hoped doesn't gain public acceptance, is the spelling as 'mute point'. This is a simple mistake, deriving no doubt from the fact that 'moot' is an archaic word with little other usage apart from in 'moot point' and that 'mute' makes some sort of sense when allied to the 'not worth discussing' meaning. This mistake isn't restricted to recent years. The earliest example of it that I can find is from John Hutchinson's Philosophical and Theological Works, 1749.