This is presuming a German military defeat of the Soviet Union within two years, but not of the UK (which I consider even more impossible). My descriptions apply to 1950's and early 1960's Europe - anything further than that is basically impossible to describe for reasons that will become clear.
Politically, the European continent would have been utterly dominated by Germany. There would be other "governments," but they could only act as Germany permitted them to do so - Italy, Spain, France, Hungary, Bulgaria, Romania, Finland, Portugal, Slovakia, and Croatia would exist. Italy would have significantly more independence. Most of the rest of the continent would have been annexed by the Reich or by Italy - Switzerland might or might not exist, Sweden probably would remain independent, Norway might be independent but under German control.
Ethnically, Europe would be virtually rid of Jews and Romani, while most Slavs (Russians, Poles, Ukrainians, Czechs, Serbs, etc) would be either slaves (some real, some effectively) or dead. Non-Germans would be second-class, with some having somewhat elevated status (Dutch, Danes, Norwegians, etc).
Militarily, German domination is virtually total. The non-German independent governments under Reich control would have small and weak national armies whose purpose is to protect the Reich and enforce submission among the populations - these forces would often be deployed away from home to further reduce the risk of revolt. For example, there would be a small French army, armed with obsolete weapons, and with large portions of its forces deployed in Yugoslavia or Greece or Denmark to fight partisans or man coastal fortresses.
The German Army has been replaced by the Waffen-SS, which is armed with well-engineered but often overly-complicated equipment (tanks based on the Panther and Tiger I). This force is highly political - promotion is generally based on a soldier's loyalty to the Reich and the Nazi Party's ideals, along with "performance" against partisans in the former USSR - those officers most effective at slaughtering civilians would be promoted over those who are competent administrators at home. The Waffen-SS has occupation forces all over Europe. It is an inefficient, exceptionally brutal, and exceptionally fanatical killing machine.
The Luftwaffe remains independent but also highly politicized. It is primarily composed of first-generation jet fighters and light bombers, plus a large fleet of heavy bombers - prop fighters continue in service for anti-partisan duties. Imagine the 1950's Soviet Air Force - this is what the Luftwaffe would look like. The Kriegsmarine has been rebuilt, but most of its combat ships are out of date - only the submarine service is truly modern.
Economically, German firms dominate Europe, and the rest of the continent is organized so as to enrich the Reich. Exchange rates favor the Reichsmark (which is accepted everywhere), occupied countries pay the cost of their occupation (thus paying for large parts of Germany's military budget), German products have favorable customs rates (making them cheaper abroad and protecting German industry from competition), German firms own favorable concessions on natural resources and many foreign industries, and so on. Much German industry and agriculture is produced via slave labor, who are exterminated through backbreaking work. Germans themselves enjoy plenty of jobs but find it difficult to get high-quality goods - they're poor and don't realize it, since the rest of Europe is much poorer.
Culturally, Europe has been raped. Much of the art of centuries has been looted and sent back to Germany or has been destroyed. Nazi architecture and art abound - grotesque monstrosities designed for their size and aggression. Berlin itself is being rebuilt according to Hitler's plan - its palaces replaced by giant, hideous buildings. All film, theater, and music is propaganda.
In the former USSR, the partisan war there makes the war in Vietnam look like a Sunday School. No quarter is expected or given - prisoners on either side are tortured and executed. Any females, of any age, captured are repeatedly raped and killed by their captors. Any civilians living in the area are subject to extermination by either side, often just for living within miles of a partisan group or for being German settlers. Massive plantations, protected by the Waffen-SS, hold slaves for agricultural work - their model is the American South prior to the Civil War, but made far, far worse. This area is a permanent fighting ground for the Waffen-SS, to "improve" the German people through constant struggle and provide a testing ground for new weapons. The cities of the USSR have been razed, their cultural achievements destroyed and expunged from memory.
Britain remains independent and anti-German. It is heavily militarized - the Royal Navy is the second largest in the world, the Royal Air Force the third largest. The country is literally covered in anti-air weaponry, the Army is massive and very well-equipped, and the people are relatively poor due to the massive costs of national defense but remain better off than those on the continent. Rationing continues. Britain remains in a watchful peace with the Reich, and is permanently allied to the Commonwealth and the United States (also heavily militarized, as much or more so than it was in the 1950's).
Britain and the United States own a total monopoly on atomic weapons (the German atomic program being a total failure), and keep them a secret (German espionage being an utter joke throughout the war). If war breaks out again, German cities will face nuclear fire with no way to strike back.