What does "burned the station brand into our walking sticks" mean?

Question

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?

Answer 1

It's difficult to be certain without more context. But the words make literal sense. A brand is literally an identifying mark that is burned onto a surface. Typically this is done by heating a metal die that has the mark, then applying the die onto the receiving surface. Livestock are often branded in this way. When sheep graze in common pasture, flocks from different farms mingle together, but when it's time to separate those flocks and return them to their farms, the brand helps identify the owners.

In this case, the walkers move ahead from one station to the next during the night. At each station, a clerk burns the identifying mark for that station into the walkers' sticks. This attests that the walkers have been there. So the brands provide "proof of our progress through the darkness".