1) A stratum or seam of coal.
The analogy is with the veins in the human body which are evidently different from the ‘material’ in which they are set. References to ‘vein’ in connection with mining occur from the fourteenth century but are almost always to metals such as gold and tin. Typical examples which refer to coal in Yorkshire date from the fifteenth century: 1464 veynes of cole in the manor of Skipton
1538 Ther be some Vaynes of Coles found in the upper Parte of … Richemontshire
1683 the Seem or Veine of Coale where you have caused to be diggid goes directly underneath it [the church], Whitkirk.