What technology made trench warfare obsolete?
I would say the Tank:
Trench warfare is a static way of fighting and relies upon the fact that the two opponents face each other occupying fixed position and attacking each other from these positions trying to inflict as many casualties as possible to the enemy without really caring about territorial gain.
The battle of Verdun during WWI is a classic example of this idea; the battle was a "meat grinder" where territorial gain was even discouraged!
The Tank, introduced in WWI, produced a dramatic change even in the mentality of the combatant; now war was waged in motion through fast and violent thrusts forward (Blitzkrieg) to penetrate enemy lines, create chaos, panic and disorientation in the rear of the enemy positions (possibly still held by the enemy) and allow the infantry to flood the rear of the front and encircle huge enemy formations that in this way are isolated, starved and pounded causing their surrender (operation Barbarossa: German panzers produced huge penetrations in the Russian front allowing huge encirclements).
[WWI tank Mk.1 Male]
I partly agree with the previous answer, but I think its a bit of a simplification
What made trench warfare obsolete? Well static linear defence wasn't made obsolete, it evolved, and existed in both WW2 and Korea, Trench Warfare evolved during WW1 too, the highly linear defences constructed by the Germans in the great withdrawl after the first battle of the Marne were very different from the in depth defensive positions of the Hindenburg line, and the attacking tactcs evolved as well from the "over the top at dawn" of 1915-16 to the "bite and hold" tactics of the British of 17-18 and the Sturmtruppen tactic of the German army of 1917-18
The Tank itself was a big step forwards but it was introduced in 1916 and the war carried on for another 2 years, so the Tank itself cant claim credit on its own.
What was needed was the tactical doctrines and mutual and interlocking support from all the combat arms that made linear static defences vulnerable (not obsolete) in the Hundred Days Offensive of 1918 which saw the allies breaching the Hindenburg lines and make territorial gains that were only dreamt of of in 1917 - that was delivered by the arrival of Combined Arms - where Infantry, Tanks, Artillery and Tactical Airpower were coordinated and controlled
So I would argue that it was combined arms doctrine that rendered linear trench warfare obsolete but that defence strategy also evolved but never got back to its position of supremacy it held between 1915-17
If we look at WW2 the biggest linear defence system was the Maginot line - But its failing was it was not continuous and allowed the Blitzkrieg to go round it, if the Maginot line had extended all the way to the English Channel (as was planned) the battle of France would have been at least very much longer and costly possibly very different