fired clay: baked earthenware pottery, and the broken shards left when it shatters
This is the cheapest, most common stuff of the ancient household: clay shaped on a wheel and baked hard into pots, jars, bowls, and lamps. The word covers both the whole object and its remains. An intact piece is earthenware, an "earthen vessel"; the same word names the sherds once that vessel breaks. One substance, seen whole or in pieces.
The two senses are simply two states of the one material. Nothing changes about the clay when a jar cracks; the shard is the pot, only broken. So the ancient reader heard no shift in meaning between an unbroken "earthen vessel" and "a potsherd," and this range sits comfortably under a single meaning.
What makes the word so useful for writers is what earthenware is like: cheap, breakable, and worthless once shattered. Job scrapes his sores with a jagged piece off the ground. A throat parched with thirst is "dried up like a potsherd." Fine children once worth their weight in gold are now "reckoned as clay jars." The image always trades on how ordinary and fragile the material is. The nearest raw-material words point the other way, to the wet stage: the potter's חֹמֶר is the soft, pliable clay before firing, and טִיט is mud and mire underfoot.