In the The Scottish Middle March, 1573-1625: Power, Kinship, Allegiance, Anna Groundwater calls currours "forest rangers", but doesn't actually describe their role.
I think the better description would be couriers or messengers, a description that's supported from the following passage from William Caxton's The Game and Playe of Chesse (1474):
The corrours and berars of lettres ought hastely and spedily do her viage that comanded hem/ with oute taryenge/ For their taryenge might noye and greue them that sende hem forth/ or ellis them to whom they ben sent too/ And torne hem to ryght grete domage or villonye/ for whiche cause euery noble man ought well to take hede to whom he deliuere his lettres and his mandements/ and otherwhilis suche peple ben Ioghelers & dronkelewe/ And goon out of their waye for to see abbayes and noble men for to haue auantage And hit happeth ofte tymes/ that whan suche messagers or currours ben enpesshid by ony taryenge/ That other currours bere lettres contrarye to his/ And come to fore hym/ of which thinges ofte tymes cometh many thinges discouenable of losse of frendes of castellys & of lande & many other thinges as in the feet of marchandise &c. And otherwhile hit happeth that a prynce for the faulte of suche messangers lefeth to haue victorye vpon hys enemyes/ And also ther ben some that whan they come in a cyte where they haue not ben to fore/ that ben more besy to visyte the Cyte and the noble men that dwelle theryn/ Than they ben to doo theyr voyage/ whyche thynge they ought not to doo/ But yf they had specyall charge of them that sente hem forth so to doo. And also whan they be sente forth of ony lordes or marchauntes they ought to be well ware/ that they charge hem not wyth ouer moche mete on morenynges ne with to moche wyn on euenynges/ wherby her synewis and vaynes myght be greuy/ that they muste for faute of good rewle tarye But they ought to goo and come hastely for to reporte to their maistres answers as hit apperteyneth And this suffisen of the thynges aboue sayd.
Richard Grafton's A Chronicle at Large (1568) mentions currors several times, but doesn't explicitly describe their role. However, from the following passages it's clear that they weren't specific to the English army, contradicting the Wikipedia article:
The Frenche king had his currours in the Countrie, who brought him worde of the demeanor of the Englishe men, then he thought verily to have closed the king of/England in betweene Abuile and the river of Some, and then to have fought with him at his pleasure. And while the French king was at Amience, he appoynted a great Baron of Normandy, called Sir Godmar du Foy, to go and keepe the passage of Blanche taque, where the English men must passe, or else in none other place: he had with him a thousand men of armes, and sixe thousand a foote with the Genowayes. And also he had with him a great number of the men of that Country, and also a great number of them of Mutterell, so that they were a. xij. thousaude men one and other.
The Scottes passed by without offeryng of any assault, and so went forth brennyng and destroiyng the Countrie of Northumberland, and their Currours ran to Yorke, and brent as much as was without the walles, and returned againe vnto their host, which then was within a myle of newe Castell vpon Tyne.
The Queene of England who desyred to defend her Countrie, came to newe Castell vpon Tine, and there taried for her men, who came dayly from all the partes of the Realme.
When the Scottes knewe that the Englishmen were assembled at new Castell, they drewe thetherward and their Curronrs came runnyng hefore the towne: and at their returnyng they brent certeine small Hamlets thereaboutes, so that the smoke therof came into the towne of new Castell. Some of_the Englishe men would haue issued out, to have fought with them that made the fyre: But the Capitaynes would not suffer them to go out.
And they had not bene there the space of an houre, but they sawe certein Currours of the'Scottes well horssed, which came to viewe the Englishe hoste. And when these Currours had well aduised the number of the English men, then they returned to their maisters, and shewed them all that they had scene, and sayde: Sirs we haue ridden so nere to the English men, that we haue well aduised and considered all their doyng: And we saye vnto you, they are ready abidyng for you in two fayre battailes. in a goodly plaine, and in euery battaile a fiue thousande men. Therefore nowe take good advice, for we approched so neere them, that they perceyued well that we were Currours of Scotland, but they would not stirre nor sende out one man to runne at vs.