The twin paradox
Two twin brothers are on Earth when one of them decides to go on a round trip to a nearby star at a speed close to the speed of light. When they meet again they'll notice that they aged at different rates. The twin that traveled is now younger than is brother.
This problem is usually called the Twin Paradox and it's one of the most known consequences of the Special Theory of Relativity. It implies an apparent contradiction with the postulates of the theory that says that any two inertial frames are equivalent and no experiment can be performed to conclude if an observer is at rest or moving at constant speed. If the trip is done at constant speed (and the U-turn is performed instantly), during the entire trip the traveling twin is in an inertial frame, except at the point where he reversed his motion. Therefore, there should not be any age difference when they meet again.
In this talk the tale of the two brothers is told and it's shown that there actually is an age difference when they meet again, but especially that this age difference doest not contradict the postulates. It is contrary to our intuition but doesn't constitute a logical paradox. On the contrary, any experiment that they can perform will result in a perfectly symmetrical result and none of the twins can claim to be at rest while his brother travels.
This talk is given at a very elementar level, avoiding any calculations and explaining the principles of the theory by using diagrams. For that reason, it can be followed by high school students, without any knowledge of relativity, or by the general public.
We can't say the same about the consequences of special relativity. It can really blow our minds!