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The speed won't increase; the penalties will simply be removed. The speed, or rather, the Movement Points, doesn't change throughout the day :D. More accurately, it decreases with each step. ;)
Speed is the "walking distance." The "walking distance" increases when you dismiss pikemen, i.e., the warriors that impose a penalty when crossing a swamp. AmberSoler;93440
You can remove the penalties during the current day by removing the units that slow you down on rough terrain from your army... And that's why the speed increases...
In other words, the distance the hero can cover in a turn increases.