Weaving is a binary decision made over and over: at every crossing, is the warp thread on top or the weft? Nothing else happens. A four-shaft loom lets you make that decision in four different ways, and every pattern in the history of cloth — twill, satin, basket, overshot — is one of those four sequences played out.
The threading says which shaft each warp thread is heddled on. The tie-up says which shafts each treadle lifts. The treadling says which treadle is pressed for each pick of weft. The cloth that comes off the loom is what happens when those three grids are multiplied together — and it is drawn here exactly that way, one crossing at a time.
Change any one of the three and the whole cloth changes, which is why a weaver's draft is the design. The pattern exists on paper first, and the cloth is the consequence.
A float is a run of the same thread over the crossings. Long floats are soft and lustrous but weak and snaggy; short floats are tough and stable but dull. Almost every decision in weaving is a negotiation between those two, and the words in the trade — sateen, twill, rep, gauze — are mostly names for where on that scale a cloth has been put.
Plain weave, one over one under, is the oldest and the most stable, because every crossing binds the cloth in both directions. Twill floats the warp over two or three and makes a diagonal. Satin floats long and scattered, and is the one that lets the light lie flat.