Abarim Publications' online Biblical Greek Dictionary
The noun υλη (ule) means basic matter or elementary matter: the stuff something is made from. In the older classics, this noun refers to wood — our noun derives from the Proto-Indo-European root "swel-", meaning both wood in the sense of forest, and wood the material (hence too the English word sill and the familiar Latin word silvas, hence our English adjective sylvan, or pertaining to woods) — but as wood was a primary building material from which people made houses, furniture and even utensils, our word began to be used to denote any basic material.
Wood, of course, was also the primary fuel of people, and as we discuss in our article on πυρ (pur), fire, a society was centered upon and organized around its fire. At night the fire kept wild animals at bay, and kept people warm and provided them with light. In other words: where the noun δενδρον (dendron) predominantly denotes a living and natural tree, and the noun ξυλον (xulon), mostly a chopped or worked piece of wood, our noun υλη (ule) emphasizes the constructive wood that literally sat at the heart of society, and kept it all together.
In the classics our word could denote any sort of wood — from huge trees and large beams to bushy undergrowth and the twigs from which birds weave their nests — but mostly specifically referred to building material. Strikingly, the philosophers and poets adopted our noun to describe the subject matter of a piece. Later still, our word began to be used opposite the noun νους (nous), meaning mind, or the intelligent and formative principle that weaves any stack of independent observations and other loose subject matter into a single building.
In modern Greek, this word means matter (as in molecules and atoms), which is rather apt, since our modern word atom comes from the Greek noun τομη (tome), which generally denotes a thing split down to its most basic remainder and specifically a tree stump left standing after the tree itself was felled.
Our noun occurs in the New Testament in James 3:5 only, in the sense of wood at the core of a fire, in an obvious but perhaps hard-to-believe reference to the fundamental structure of an atom; see our article on the name Silas for more on this. Our word has no derivatives, but note the striking similarity between the Latin branch of this PIE root and the Hebrew root סלל (salal), to heap up (hence words meaning highway and basket).