You’ll notice as you move, the Mv number next to your unit in the Stack List is going down. The exact amount it goes down varies with the terrain it moves into. This is what the Move Cost value in information displays tells. Obviously, if you don’t have enough move points to move to any adjacent square, that unit is finished moving for the turn. They all get their move points refreshed at the end of the turn for use next turn. (see Move on the Player Info Window or Army Info Window)

When I moved my caravan close enough, the Ape-Men appeared on the screen, I'll move in for the emissary.