Granted that tanks alone are only a fraction in the equation of what made the German army advance so quickly in enemy territory, mechanical warfare must have been played a large part. Especially when tanks were a cornerstone for the development of blitzkrieg tactics, from what I understand. I've also read that tank vs tank engagements were rare, especially during the early stages of the war, but it still doesn't add up to me. How could German tank divisions seemingly (to the novice reader) drive deep into hostile territory without being slowed down significantly by superior enemy tanks?
From what I've read, the Germans were considering fully reverse engineering the T-34 tank, as they considered it superior to the Panzer III and IV's, but ended up developing the massive Panther and Tiger tanks instead, along with modifying the IV to match the T-34 better. Guderian apparently labled the T-34 "vastly superior" and von Kleist " the finest tank in the world".
Not related to question per say:
I tried searching around for a similar answer on here, but I couldn't any that talk about German advance, rather than purely tank statistics and realibility. Two answers I found helpful, but didn't quite answer my question: Answer 1 - Answer 2
When I was 17 I wrote a history essay on Operation Barbarossa, where I learned that motorcycles, horses, and regular bicycles where influential for German troops to cover a large distance in a day. I also remember reading the army encountering Soviet troops still training. It seemed that the German army moved virtually unapposed until they were a few kilometers from Moscow in the North and deep into Ukraine in the south. I believe our source relied heavily on the writings of Guderian, which are understandably biased and also credited for influencing the "clean Wehrmacht" myth. That narrative is still a stark contrast from stories of difficult engagement with the T-34 and KV tanks and heavy Soviet resistance in general.
So there are a lot of Operational things the German army is doing right against France and the Soviet Union. However in this answer I'm going to focus on tactical strengths of the German army meaning the way it fought at the Division/Regiment/Battalion level.
Combined Arms expertise is one of the things that separates the Germans from their opponents tactically. Combined arms is the ability of different unit types: e.g.Tanks, Artillery, Anti-tank guns and DP anti-aircraft, Infantry and Aircraft to cooperate with each other and bring their strengths to bear against the enemy's weakness.
Panzer Divisions were effective Combined Arms teams in 1940-41. Their table of organization contained a good mix of tanks units, motorized infantry units, artillery units and anti-tank units. The French armored units tended to be much more tank heavy, so the tank battalions could not call on as much artillery support or infantry support as they needed. German anti-tank assets, especially 88mm DP Anti-aircraft batteries were also better integrated in Panzer divisions. Soviet armored units were in theory combined arms oriented, but in practice doctrinal shifts in 1940-1941 meant that these units were not well organized in Summer 1941.
In addition to just having combined arms assets, there are two other elements that make them work together well, radios and air support. The most important equipment advantage German armored forces had was radios in the tanks, which French and Soviet forces mostly lacked. This allows Panzer units to effectively coordinate with artillery, anti-tank and infantry units. But it also allows them to communicate with Aircraft and reconnaissance units, and have a better situational awareness of what was happening over the next ridge. Enemy aircraft are also very disruptive to combined arms, airstrikes are particularly good at locating and striking vehicle units on roads and artillery batteries firing in support positions. The Germans had a reasonable superiority of air in France, and overwhelming air dominance in the Soviet Union. Plus the German attack aviation (Stuka's etc.) was just more practiced at hitting targets and coordinating with ground troops.
Lastly, the German forces generally had more combat experience than their French and Soviet opponents in 1940-41, so their regiment, brigade and division commanders had more practice putting the right combined arms asset on the right target.
By using combined arms, the Germans were able to confront Char Bs, Matildas I and IIs, T-34s and KV tanks. These tanks may have been superior to German armor, but if the Germans could put an 88mm DP AA gun, a 15 cm howitzer, or a Stuka against them it was a contest the Germans could usually win. These assets can't be everywhere though and they can themselves be vulnerable, so communications, agility and flexibility are essential to make sure the right piece is in the right spot at the right time.
This answer is also glossing over operational, strategic, morale and political considerations which I acknowledge as important but will have to be tackled by someone else.
Sources:
Karl-Heinz Frieser The Blitzkrieg Legend: The 1940 Campaign in the West
Robert Forczyk, Tank Warfare on the Eastern Front 1941: Schwerpunkt