Sounds like a silly question I know. Presumably it gives a unit, well, better stamina than those without the trait. But I did a quick experiment in a custom battle where I made one unit with "good stamina" and one without repeatedly run back and forth across the map and there appeared to be no difference in how quickly they tired. To clarify, I mean that their statuses changed from "fresh" to "warmed up" and from "warmed up" to "winded" within a couple of seconds of each other. I put this small difference down to my timing in issuing the commands and that the routes wouldn't have been identical.
Does good stamina just give soldiers greater endurance when fighting, and not when travelling?