Essentially:

The BEF (British Expeditionary Force), some remnants of the Belgian army and some French armies were cut off from the rest of the allied forces further south when Germany made a rapid advancement through the lightly defended Ardennes (the allies had wrongly assumed the Ardennes to be unsuitable for an offensive).

The commander of the British Forces immediately took action to evacuate through the channel ports, Dunkirk was the closest of such ports that had the facilities for such an endeavour.

Hitler ordered a halt and German forces stopped advancing, giving the allies time to build defenses around the city and pull more men and material back to Dunkirk.

This Halt Order is an area of contention and there are many theories around why Hitler did it. Some argue the German army needed time to resupply, rest and reorganise. Others argue the Panzer units had outrun the infantry and supply lines and couldn't mount an offensive until these elements had caught up with them. Some think Hitler assumed that once the British army left the continent, it would not be able to return and thus of little significance with Paris ready for the taking.

In any case, over a period of days Navy ships and commandeered and volunteered civilian ships made several trips ferrying men out of Dunkirk. In total it as about 300,000 British and French soldiers who were rescued. At first preference was given to the British, but they were given equal footing for evacuation. Throughout this time however British and French forces were fighting rearguard actions against the Germans, many of these units would eventually surrender once the evacuation was complete and spent the rest of the war in POW camps.

The Luftwaffe strafed and bombed the soldiers waiting to be evacuated, however, the RAF were able to inflict some reasonably significant losses.

Most of the men got out, but a huge amount of equipment was lost, especially tanks, trucks, and heavy weaponry. The operation rescued thousands of french troops, who were quickly redeployed in France, though some later joined the Free French army, as they couldn't get to France before it capitulated.

It is often mythologised in the UK due to the use of civilian ships, often captained by civilians as an example of civic duty and the spirit of the war, however it was largely a narrow escape from a military catastrophe. Had the UK been unable to evacuate the BEF the voices calling for a peace with Germany might have been listened to with greater enthusiasm.

Not to discourage any newer answers, but you may be interested in this recent thread, particularly the answer from u/thefourthmaninaboat.