Short answers, pulled from the story.
Operation Market Garden aimed to create a 62-mile Allied corridor into German-occupied Netherlands, capture nine bridges using airborne forces, and establish a bridgehead over the Lower Rhine at Arnhem. Achieving this would have opened an invasion route into northern Germany and bypassed the Siegfried Line.
The British 1st Airborne Division landed too far from the Arnhem bridge, with only a fraction of its strength able to reach the objective in the first lift. Radio communications failed almost immediately due to wrong frequencies and limited range. The II SS Panzer Corps, with the 9th and 10th SS Panzer Divisions, was refitting in the Arnhem area and responded faster than Allied planners had anticipated. Warnings about the SS armour, including aerial photographs taken on the 12th of September 1944, were dismissed by senior commanders.
The airborne force numbered around 35,000-40,000 men, with over 34,600 delivered by glider and parachute during the operation. The British Second Army's land component included approximately 50,000 soldiers with around 800 tanks across ten armoured and motorised brigades. About 100,000 German soldiers were in the vicinity to oppose the offensive.
The British 1st Airborne Division suffered 8,000 dead, missing, and captured out of a complement of 10,000 men. When the retreat order came, there were not enough boats to bring everyone back across the Rhine. Some soldiers evaded capture with Dutch underground assistance and were rescued in Operation Pegasus on the 22nd of October 1944.
Lieutenant-General Brian Horrocks commanded XXX Corps, which spearheaded the ground advance up Highway 69. The overall land operation was conducted by the British Second Army. The airborne component fell under Lieutenant General Lewis H. Brereton's First Allied Airborne Army, with tactical command exercised by Lieutenant-General Frederick Browning's I Airborne Corps.
Arnhem was finally captured by the Allies in April 1945, towards the end of the war in Europe. Operation Market Garden itself ran from the 17th to the 25th of September 1944 and failed to secure the Rhine bridge there, extending the campaign in the Netherlands by months.