"I know what it is but I cannot explain it." That sums it up for me and as the
Wikipedia entry does not provide much help . . .
I will try all the same:
The Silver Age of comics was the time when comic books shifted to being more about the people with super-powers rather then the super-powers themselves. It was also the era of pseudo-scientific explanations for how characters gained their powers, most of the super-powers of the Golden Age of comics were mystical in origin (i.e., Wonder Woman's equipment, the 'magic word' SHAZAM that transforms Billy Batson into Captain Marvel, the Specter and Dr Fate) but the Silver Age sees science and especially radiation --radioactive spiders, cosmic ray, gamma radiation-- as the source of new super-powers.
The Silver Age is still, essentially, optimistic about people and what they can, and will, do. Science
will solve all our problems. The US is the greatest force for good on the planet. Those foreign powers (communism had receded but not vanished as a threat in the comic books) would see the light and become happy mixed economy democracies, just like us. Supervillains tended to be money-grubbing, just plain crazy or dictatorial, very few had political agendas beyond personal power, and fewer still were painted in shades of grey. The world was still very black and white (and four color).
But clouds were gathering on the horizon of the Silver Age, the war in Vietnam, the upswing of drug use in the US, the fracturing of American society as the new anti-war, anti-capitalist left emerged among the college students. It was a time of change and transition.
All of the above are what make it such a fun period to play Superhero RPGs in.