This classification must have originated from the way the Upanishads' "importance" are described in the Muktika Upanishad (linked to Shukla Yajurveda), which lists the names of the 108 Upanishads.
Hanuman: How many are the Vedas and how many branches do they have ?
Of these what are the Upanishads ?
Rama: Vedas are four, Rig-Veda etc., many branches and Upanishads
exist in them. Rig-Veda has 21 branches and Yajus has 109. Sama has
1000 and Atharva has 50. Each branch has one Upanishad. Even by
reading one verse of them with devotion, one gets the status of union
with me, hard to get even by sages.
I-i-15-17. Hanuman: Rama, sages speak differently: some say there is
only one kind of liberation. Others say it can be got by worshipping
your name and by the Taraka mantra at Kashi. Others speak of
Sankhya-Yoga and Bhakti-Yoga, the enquiry into Vedanta-Vakyas etc.
I-i-18-23. Rama: Liberation is of four kinds: Salokya etc. But the
only real type is Kaivalya. Anybody even though leading a wicked life,
attains Salokya, not other worlds, by worshipping my name. Dying in
the sacred Brahmanala in Kashi, he will get the Taraka-mantra and also
liberation, without rebirth. On dying anywhere (else) in Kashi,
Maheshvara will utter the Taraka-mantra in his right ear. He gets
Sarupya with me as his sins are washed away.
The same is called Salokya and Sarupya. Persevering in good conduct,
with mind fixed upon me, loving me as the Self of all, the twice-born
gets nearer to me – This is called the three forms of liberation.
Salokya, Sarupya and Samipya.
I-i-24-25. Meditating on my eternal form as prescribed by the Teacher,
one will surely achieve identity with me like the insects changing
into the bee. This alone is the liberation of identity (Sayujya)
yielding the bliss of Brahman.
All these four kinds of Mukti will be got by worshipping Me.
I-i-26-29. But by what means is the Kaivalya kind of Moksha got ? The
Mandukya is enough; if knowledge is not got from it, then study the
Ten Upanishads. Getting knowledge very soon, you will reach my abode.
If certainty is not got even then, study the 32 Upanishads and stop.
If desiring Moksha without the body, read the 108 Upanishads. Hear
I-i-30-39. 1. Isa
As you can see, according to Muktika, the highest knowledge is obtained from Mandukya alone. If that is not possible, then recommendation is to study the (first) ten (in the list given). From this people have probably concluded that those 10 are the principal/major (Mukhya) Upanishads and the rest are Gaunya or minor. However, in reality most people consider not just 10 but 12/13 Upanishads as major.