It refers to all those things that look impossible to achieve until somebody proves that they are not.
According to the RAE (Real Spanish Academy dictionary), the egg of Columbus is defined as something that apparently entails big difficulty, but which ends up being easy as one gets to know the trick behind it.
This definition alludes to an edible egg that Christopher Columbus used in a demonstration at a dinner with the Spanish nobility, during which he bet that none of the people that were present would be able to make an egg stand on its tip. After everybody tried with no success, Colombo managed to make it stand by tapping it gently on the table and slightly breaking it.
This way, he attempted to explain that something that seemed impossible could in fact prove easier once you understand how it works.