We actually do know a lot about it.

The halt order originated at Army Group A and 4th Army headquarters the day before it was given (the halt order was given on May 24). Von Rundstedt, von Kluge, and von Kleist, faced with an amazing possibility of victory, simply lost their nerves. They did not think that the armoured divisions would be able to hold their corridor to Dunkirk had they struck for it. The Battle of Arras (May 21) had already made them nervous about this. Hitler only got involved when von Brauchitsch took the 4th Army and gave it to von Bock so he could direct the encirclement.

When Hitler found out, he was infuriated. He gave the army back to von Rundstedt, and quite clearly left the future course of operations to Army Group A. Hitler was convinced by von Rundstedt to stop for a bit. In any event, the fighting didn’t just end. The German infantry was still in motion fighting the Allies across the pocket’s perimeter. In the subsequent Fuhrer Directive, Hitler demanded the annihilation of the trapped Allies.

It should be noted that the war wasn’t in its final stages in the Dunkirk battles. The Germans still needed their armour for Case Red. Von Rundstedt, a military conservative, had never been a huge fan of the Sedan breakthrough in the first place. Exposed flanks and lightning speed was simply too edgy for him. They also still had to defend against the south; the French below Army Group A were still there, they hadn’t disappeared.

The Battle of France was still an amazing victory for Germany, with or without the halt order. But of course, after the war, the German generals all blamed Hitler for the Miracle of Dunkirk in their memoirs. The fact of the matter is that it was a military decision. It wasn’t even evident to the Germans that the Allies had gotten a huge break at the time. When the halt order was rescinded, the Allies were still in a very desperate situation.

People have used the old cliché that Hitler "let" the British escape in order to make peace with them. Apart from being militarily nonsensical, since destroying your enemy’s army would be the surest way to compel his surrender, it isn’t convincing. Part of the reason seems to be that the French are so maligned and so easily dismissed in retrospect that people forget that they were still present. The French forces essentially sacrificed themselves so the British could escape, establishing a strong collapsing perimeter around Dunkirk until forced to surrender (after the British had mostly managed to pull off Operation Dynamo).

Secondly, the curious thing about the German drive is that the Germans were not aware of how successful they had been. They kept expecting to run into the "inevitable" French counterattack, haunted as they were by the Marne. They still imagined the French had powerful reserves they were waiting to spring upon them, unaware that they had practically disembowelled the French Army.

Sir Ian Kershaw, when asked specifically whether Hitler allowed the BEF to escape, answered: "Hitler himself created this myth in the sense that he used it as a justification subsequently for why the tanks were not sent down to destroy the British Army at Dunkirk. But in reality what Hitler was doing there on the 24th of May 1940, that crucial day, was actually agreeing to the suggestion put forward by the commander of the German forces in the West – General, rapidly to become Field Marshall, von Rundstedt – who then wanted to preserve the tanks for what they saw as their greater need which was to destroy the French troops by moving South against them. And Goering had promised Hitler that the British troops would be bombed to bits from the air anyway. So for 24 hours Hitler went along with that decision, realised subsequently it was a mistake and then backtracked from it, but by then it was too late and the British were on their way to getting away from Dunkirk. But it was actually Hitler at that stage still going along with the advice of his Generals, not overriding it as he came to do increasingly as the war went on."