The term selvage (or selvedge, for the Brits) comes from the phrase “self-edge,” and refers to the self-finished edges formed when the cross-thread (or weft) loops back into the lateral thread (or warp) on each side of a bolt of fabric. It can appear on any type of cloth, but you’re most likely to encounter it when you pull on a pair of jeans.
And when it comes to denim specifically, it means that the fabric was woven on an old-style shuttle loom that weaves the denim with a continuous weft. Unlike modern projectile looms with multiple wefts—the kind that most jeans manufacturers started using around the 1950’s to keep up with demand—shuttle looms yield a narrow bolt of fabric (typically around 30”). Narrower bolts mean a longer piece of fabric is needed to make a pair of jeans. Couple that with the relative scarcity of functional shuttle looms, and you’ve got a more expensive final product.
Nevertheless, diehards swear by it. Why? For one, the use of a continuous weft tends to create denim with more irregularities and a greater depth of character. Also, making selvage denim is time consuming, and it requires specialized equipment. Simply put: It’s a chore. If a mill is willing to put in the time to weave it, and a company is willing to put in the expense to produce jeans from it, it’s often (though by no means always) an indicator of a higher quality product.