I answered a question very similar to this here about 6 months ago, but I'll give an answer that's more relevant and add more information.

The director of Fury, David Ayer, chose to make the movie quite gritty and brutal to show the realities of war, stretching a few historical realities a bit far to fit them into a two-hour film that covers the course of one day. Some of the elements of the film, such as the supposed massive losses taken by armored crewmen, (a trailer for Fury makes the claim that the average lifespan of a U.S. Army tank crew was 6 weeks) are somewhat unsubstantiated, and taken from popular history such as Belton Y. Cooper's book Death Traps: The Survival of an American Armored Division in WWII (in part what inspired Ayer and what Fury takes some of its material from) which is often criticized by historians for being unfairly biased and technically inaccurate. Related urban myths and simple misinterpretations of period documents have also cemented themselves in the minds of the public, being repeated often.

The Army experienced a manpower crisis in its combat arms beginning in late 1943 that most severely affected the Infantry branch. A heavier than expected casualty rate hit combat arms after the invasion of Italy in September of that year. Replacement training centers were unable to quickly keep up with changing battlefield conditions as the training cycle was repeatedly lengthened, and ham-fisted responses by War Department authorities led to shortages of men in many combat arms specialties. A lack of a reasonable proportion of men (one that properly reflected the astronomical casualty rate of frontline infantry) specifically trained as riflemen being shipped to replacement depots plagued many units. The problem steadily worsened when the Army relaxed its induction standards in mid-1944; even arms with comparatively low casualty rates such as armor were complaining about the poor quality of trained personnel they were receiving! (rejection rates at combat arms replacement training centers in late 1944 for physical and mental unsuitability ran as high as twenty percent) The problem hit its peak in the fall of 1944 and continued until the late winter of 1945, by which time it was mostly resolved by taking drastic measures, such as stripping troops from divisions still in the United States, retraining troops with certain specialties from already-arrived divisions, and combing rear areas for physically-fit men serving in positions that could be filled by men not suitable for frontline combat duty.

Casualties in the Armored Force were lighter than is commonly imagined (due to fighting an offensive war against an entrenched enemy, vehicle losses were high, however) and they were not affected as badly by this crisis. In tank units that were particularly aggressive, or were in the line for long periods of time and could not withdraw, there did exist retraining of men who were already within the unit when replacements could not be brought up in a timely manner (the “lag time” after submitting a request was on average six to seven days) When units of all stripes got unlucky and encountered a replacement shipment that had already been “cleaned out” and did not contain enough men of a certain specialty (all too common in 1944), men in any specialties, usually ones at least close to the ones desired, (many specialties had acceptable substitutes listed) were selected to be retrained. In tank units, these men usually filled spots that did not require much experience, such as the loader or bow gunner’s position. For skilled crewmen like commanders or drivers, a temporary decline in combat power until a proper replacement could be had was almost always preferable to an inexperienced soldier commanding a $45,000 medium tank and four other highly trained men. This was not a universal practice, and peaked in fall 1944 and after the Battle of the Bulge, mostly ending by early 1945. By that time, it would be extremely uncommon for a completely untrained soldier like Norman to be forced into a tank; it is more likely that he would be reluctantly selected from a replacement depot by a unit than pulled off a truck heading to another assignment. The Armored Force replacement training center at Fort Knox produced 12,000 officers and 168,000 enlisted men during the war. After the heavy losses of the Battle of the Bulge; the Armored Force replacement training center requested 5,000 enlisted men taken from deactivating tank destroyer, airborne, and cavalry units to retrain as replacements.

Crews in armored units that frequently encountered enemy tanks felt that the automotive characteristics of their vehicles were mostly on par with German vehicles (American half-tracks, trucks, and light vehicles were said to have a distinct superiority over German ones), but were highly critical of the penetration abilities of the 75 mm and 76 mm guns against the thickest armor of the Panther, Tiger, and King Tiger with reactions varying from annoyance to outright condemnation and anger (In an early draft of the script for Fury, Gordo refers to the American tanks as "shit boxes"); an informal report prepared by 2nd Armored Division commander Major General Isaac D. White for the Supreme Commander of the Allied Expeditionary Force Dwight D. Eisenhower in March 1945 elicited mostly negative opinions on the Sherman’s ability in tank versus tank combat. A flap in the press at home occurred in early 1945 over this issue, but it was mostly ignored by high-level Army officials who felt that the Sherman was performing its intended role as one of the main tanks of the Western Allies properly and successfully.

Fury takes place in April, 1945, during the race across Germany. As the German front lines collapsed, Allied forces advanced as much as fifty miles a week, constantly on the move. As a result, divisions often moved on before a proper command post could be set up in a town; divisions often called two or three towns home in the same day! As a result, camps were often haphazard, a collection of tents (if that!) in an open area with vehicles parked nearby, waiting for the next set of orders. Sometimes, troops were billeted in houses, either abandoned or not; occupation forces had the authority to expel German civilians (but had to find accommodation for them) so that US troops could use their houses.

Boxed C and K rations (supplemented by higher-quality B rations and occasional fresh food) were the troops' primary food source during this time, as field kitchens often could not be set up due to the speed of the advance. Canned emergency rations were not supposed to be used for a period of more than about a week and a half, and their sparse nature, in relation to filling "actual food", sometimes caused serious intestinal distress (in the same draft, Wardaddy tells Bible he's going to "the latrine to take a shit" because he "ain't shit in a week"). Soldiers often supplemented their rations with local German or French food, either acquired or thieved (the kitchen scene). In a brief glimpse in the beginning of the film, a soldier leads a cow, and there are several goats in a pen.

During these quick movements through Germany, hundreds of thousands of German soldiers surrendered to the Allies, either captured in battle or simply not wanting to fight anymore, wanting to return to what remained of their homes. The captured enemies were herded to the rear and placed in massive camps particularly along the plains bordering the Rhine River. Some of the camps were only enclosed by a few strands of barbed wire, guarded by a few soldiers. The German soldiers behind barbed wire at the beginning of the movie were presumably soldiers who were captured immediately before, and waiting to be picked up and transferred further to the rear. Conditions in these camps were often less than ideal due to large numbers of men in small spaces, and many hundreds of prisoners died from exposure and diseases. Author James Bacque's book Other Losses claims a figure of "hundreds of thousands" to "over one million", through a process of purposeful deprivation of food and shelter, but the methods and figures Bacque uses to arrive at his conclusions are heavily criticized by reputable historians.