This is an excerpt (no origin given) from an ACT test:
Every thousand feet, we came to a small station constructed of tin and cement, barely able to block the wind. At each one, we noted the roof piled high with fallen rocks and felt both unsettled and reassured by this evidence of the station’s protective ability. We rested uneasily for a moment as a clerk burned the station brand into our walking sticks, proof of our progress through the darkness.
What does it mean to "burn the station brand into our walking sticks"? What does "station brand" symbolize? And why does it count as progress?