The original meaning of swatch as recorded in the Oxford English Dictionary was, “The ‘foil' or ‘counterstock' of a tally; in Yorkshire, a tally ‘affixed to a piece of cloth before it is put with others into the dye-kettle'” and was “originally Scots and Northern”.

Subsequently, swatch came to  mean ‘a sample', specifically of cloth or several samples of cloth made into a book, and the first mention of this sense comes from Older Scots in 1571-72 from the Transactions of the East Lothian Antiquarian and Field Naturalists' Society Haddington, 1924-:  â€œTo Johne Hoip for gangin to Glaidismure with the swatch … about the laird of Sammelston besynes”. However, the more general modern meaning of a sample, in the figurative as well as the literal sense, was in use as early as 1688: “His plots and practices … do give some swatch and specimen of his former craft and cruelty”,  from The Testimony of some Persecuted Presbyterian Ministers of the Gospel unto the covenanted Reformation of the Church of Scotland by J. Renwick.

In current day use it can also mean a quick inspection, a glimpse, a glance, as from Jeff Torrington in Swing Hammer Swing!: “I'd a wee swatch at The Beano, just to see how my old chums were faring in their timeless world of chortles, japes and tee-hees.” (1992).  However, the original meaning is still also found, albeit not meaning cloth but a sample of hair, as in this example from the Aberdeen Evening Express of 28 February 2015: “‘So go blonde,' Craig said, taking a swatch of hair from a cupboard. Ash blonde. ‘What do you think?'”.
Swatch can also be us as a verb, meaning to glance peep: “Gaun tae let us swatch it?” from Roddy McMillan, The Bevellers (1974).
Unfortunately, the etymology of this word is lost to us as even the OED states that this is ‘origin unknown'.
Scots Word of the Week is written by Pauline Cairns Speitel of Scottish Language Dictionaries