To my knoweldge, the biggest explosion by a bomb was the ‘Tsar Bomba’ – a Russian nuclear bomb that was detonated in 1961. It had a power of 50 Megatons – that’s compared to the first ever nuclear bomb which had a power of 20 kilotones.
If you want the biggest planned bomb explosion that WASN’T nuclear though, you have to look back to the Battle of Messines in World War 1.. huge mines were set beneath the German lines and the explosion was heard as far as London and Dublin! Scary stuff.
I would think that would have to be one of the Hydrogen bombs detonated in Japan at the end of the second world war. That would be the biggest bomb detonated in war, but I would think there have been bigger ones detonated in tests and anyone of Russia (Soviet Union), China or USA may claim that record. The old Soviet Union had a hydrogen bomb called the Tzar bomb which was supposed to be be like an explosion of 50 megatons of TNT!!!! Quite a bang. Only detonated in a test though I think!
I did a Google search, which suggests that the biggest above-ground test is the Russian ‘Tsar Bomba’ in 1961 (http://nuclearweaponarchive.org/Russia/TsarBomba.html), designed to be 100 megatons, but altered to reduce the amount of radiation released during the test. The term “megatons” refers to the amount of TNT that would release the same amount of energy. “Mega” is a prefix meaning one million. So, a full explosion of this bomb would have been equivalent to igniting 100,000,000 tons of TNT.
Why is TNT (trinitrotoluene) used as the standard comparison? Because it was a very early and important explosive. Interestingly, Alfred Nobel was into explosives: he invented dynamite a few years after TNT was invented.