The Ptolemaic system of astronomy made some very important claims about how the solar system was structured. That Earth was the center of the solar system...maybe even the universe. It claimed that the stars and the planets orbited around the Earth.
These were scientific claims and as such were subject to verification. As astronomers grew interested in the stars, they becan to examine these claims. Leonardo Da Vince, Gallileo, Kepler, Copernicus, Tyco Brahe and Issac Newton were scientists that researched and found that these claims were false. The earth was not the center of the solar system, the sun was.
The claim was falsifiable. That was important. As a scientific claim it was wrong. It was shown to be wrong, and several astronomers, physicists, and mathematicians were able to verify the experiments that showed how the claim was false, and a new claim was true.
This is the essence of science.
Can the same be said about Evolution? Can it be shown to be falsifiable? This is a critical claim. Because if it cannot be falsifiable then it is like Intelligent Design, a philosophical claim that cannot be verified, or denied.
One way to show that evolution is false would be to show that there are no variations in the human or animal kingdom. But that is not the case. Just recently there was a sad case of an Indian girl that was born with four arms and four legs. This example shows that there are genetic variations possible. But there have to be other tests to show that evolution works. Evolution as a function of genetic mutation.
One experiment would be to expose cells to radiation. If there are no genetic mutations as a result of the experiment then genetic mutation might be suspect as a vehicle of evolution. But as it is there are many cases of radiation leading to genetic mutation. This however is the falsifiability condition.