Armies don;t just move randomly, they are manoeuvring to put their enemy at a disadvantage. Imagine or watch two cats in a yard and you will get the idea.
In 1940 the Allies put most of their forces in Northern France, expecting an attack through Belgium. The Germans attacked further south, the arrow marked 'German advance'. Thus, they side-stepped the main allied armies. They then got behind them and headed north. This is the upward pointing arrow.
This cut the allied army off from central France, their supplies and reinforcements. Without fighting, they were compelled to retreat. The German plan had a further advantage- the French lines of communication went back to Paris, but the British had to fall back on the Channel coast to ensure they could retreat to England. Thus, the first phase of the battle ended with the British and some French units escaping at Dunkirk... but still there was the main French army, defending Paris, to deal with. The German army turned itself, gathered itself together, and then moved south, the two downward pointing arrows.
The French army was unable to hold and the French government was forced to make peace.
On such a small scale map, the arrows do not depict events all that clearly. Also bear in mind as the German army advanced, it 'strung out' behind marching infantry, so the advances were sort of like throwing a net. None of the arrows depict British army movements, and without some visual guide to where the allied armies were- the map in the link below, especially the third map, give a better idea of what happened.