1) Literally to herd animals with a staff in hand, that is.
1558 sub baculo pastorali, a phrase found in an early Malham court roll. It was the herdsman’s responsibility to prevent animals from crossing an unfenced boundary, and a bye-law of 1608 indicates that he might sit at the boundary, staff in hand, from morning to evening during the summer. The OED has examples of the verb from 1563 but earlier Yorkshire evidence shows that it is likely to have developed from an unrecorded noun: c.1530 the tenantes of Holmfirthe hath taken in theire owne common and putte their bestes of the common of Thirlston and kept them there with staffe herde dayly
1579 no sheepe should depasture upon or in any common grounds, viz laines or other common pastures but onely as they are driven from there owne houses or grounds to other of their owne pastures … and that without any stay or stafhirdyng of the same, Beverley
1615 watchers to staffeheard untill the fence was mayd, Brandsby. A much later reference links the practice with the East Riding Wolds: 1734 that no Sheepherd shall Staff-herd his Sheep in the Cow Pasture or in the Corn Field, Lund.