A vein was a concentration of minerals in a rock.
Veins of kelbonite ran through the mountains north of the Ba'ku village, which interfered with transporter functions. (Star Trek: Insurrection)
The father of John Frederick Paxton designed the Orpheus Mining colony to be mobile, knowing that in the mining business veins could dry up. (ENT: "Demons")
In 2268, a vein of pure tritanium was located in a scanner survey done by USS Enterprise on the planet Argus X. Upon Spock's confirming its presence during a landing party, James T. Kirk told Montgomery Scott he could mark the vein as confirmed. (TOS: "Obsession")
In 2372, a USS Voyager away team discovered a vein of pure polyferranide on a moon of Drayan II. (VOY: "Innocence")
In 2373, a Starfleet team discovered cormaline on Torga IV, one of the richest veins Jadzia Dax had ever encountered. (DS9: "The Ship")
Later that year, the Voyager tried to utilize a vein of gallicite on a Sakari planet. (VOY: "Blood Fever")
In 2376, an away team from the USS Equinox detected a vein of dilithium ore on a Delta Quadrant planet, deep enough that phasers might be needed to extract it. (VOY: "Equinox, Part II")